The city that works. That's what boosters call Chicago.

The credit for making Chicago "work" invariably has accrued to Mayor Richard J. Daley, whose death Dec. 20 plunged the city into anxiety about its future.

Under Daley, the garbage was collected and most streets were swept regularly. Strikes were rare, Chicago buses and rapid transit trains generally ran on time.

Daley left the city with an AA bond rating, meaning that Chicago can borrow money about 30 per cent cheaper than Philadelphia or Detroit.

That Chicago "worked" seemed evident to multitudes of envious visitors who arrived at O'Hare, the world's busiest airport, and were whisked along one of the world's most elaborate expressway systems into a downtown having three of the world's tallest buildings.

Yet, on ballance, Daley left no Camelot. He left:

America's most racially segregated big city, according to various surveys. To truly integrate Chicago - to make every block reflect the city's racial make-up - 93 per cent of the families would have to be relocated, according to University of Illinois urban socialogist Pierre DeVise. To accomplish the same thing in Washington or New York, 80 per cent of the families would have to be relocated.

A school system in which the average 11-year-old is 1 1/2 years below the national norm in reading ability. The longer children stay in the system the farther they fall behind. At age 13 the average pupil is two years behind. Of the city's 57 high schools, 51 are below the national average in achievement as measured by standard nationwide tests.

A number of poor neighborhoods in which the infant mortality rate equals the rate in Sri Lanka.There were 31.3 infant deaths for every 1,000 live births in Chicago overall, compared with 27.6 in Washington and 24.5 in New York, according to the latest (1974) figures available from the dDepartment of healhth, Education and Welfare.

A critical shortage of housing for low and moderate-income families. This was caused in part by Daley's refusal, even in the face of a federal court order, to allow public housing to be built in white neighborhoods and also by arson in apparent insurance fraud schemes that has destroyed hundreds of residential blocks in the inner city.

A rapidly dwindling supply of blue-collar jobs. Thomas G. Ayers, chairman of Commonwealth Edison Co. and a longtime ally of Daley, recently acknowledged: "Manufacturing jobs in the city decreased 5 per cent in the 10-year period ending in 1969, and by an alarming 21 per cent in the years from 1969 to 1974."

A judiciary widely regarded as one of the most politicized in the nation. Daley personally picked many judges whom local bar groups have labeled unfit for office. "The courts are shot through with politics and favoritism," laments attorney Alexander Polikoff, head a public affairs, law firm often at odds with the city administration. "Lawyers will go wherever they can outside Cook County [Chicago] just for a fair shake."

An electoral process in which fraud is rampant. Ward boundaries are allegedly gerrymandered. Legions of ghosts are registered to vote in some precincts. Republicans and independents have been ruled off the ballot by Daley's courts for technicalities that regular Democrats have skirted, court records show. Real astate tax breaks have been granted to major Democratic contributors, news media investigations have shown.

A tradition of official corruption that prompted Chicago Daily News columnist Mike Rokyo to suggest that the city's motto be changed from "Urbs In Horto" (City in a Garden) to "Ubi Est Meus" (Where's Mine?). The U.S. attorney's office - over which Daley lost control when the Republicans won the White House in 1968 - has indicted and won conviction of at least 75 local officials, including high ranking policemen and city aldermen.

A massive police spying apparatus that, according to a 1975 county grand jury report, infiltrated law-abiding civic and church groups and kept files on politicans, lawyers and journalists who criticized Daley. The grand jury, convened by a Republican prosecutor elected after a divisive primary fight in Daley's Democratic organization, called the spying "a grave threat to the individual rights and freedoms which are basic to our democratic society."

Daley's reputation as a fiscal expert was predicated largely on the fact that Chicago has avoided the financial problems that plagued New York.

"The financial administration of the city is as sophisticated as that of a major private corporation," says A. Robert Abboud, chairman of the huge First National bank of Chicago. "The budgeting process is both complete and broadly based. The financial reports are audited by independent accountants. Chicago securities are highly regarded by sophisticated investors outside the Midwest area."

A First National Bank research report on Chicago's economy last July commented: "On almost every measure, whether it be debt burden, day-to-day financial responsibility, or indicators of underlying financial strength, Chicago stands out as a strong, viable metropolis as compared with other large cities."

While the report made much of the fact that Chicago's credit rating is better than New York's, Philadelphia's, and Detroit's, it did not comment on the fact that the credit ratings of Los Angeles, Houston, Dallas, and Milwaukee are better than Chicago's.

Daley's critics do not credit the late mayor with Chicago's financial integrity. Rather, they say Chicago's money problems have been simple compared with those of other large cities.

Leon M. Despres, a retired alderman and foe of the Daley organization, has noted: "Chicago has a population 43 per cent as big as New York's, but its budget is only 8 1/2 per cent as big.

"It's a lot easier to avoid a spending crisis when the responsibility for services is dumped elsewhere."

New York City's budget includes $1 billion a year - almost as much as Chicago's total budget - just to support public hospitals. Chicago's public hospitals are supported by Cook County.

The state of Illinois shoulders the welfare burden here, and public colleges are the obligation of a board with taxing authority separate from that of the city. Those are municipal responsibilties in New York.

Despite inflation, Daley managed to avoid property tax increases year after year. To cover rapidly rising costs, he imposed a head tax on employees of private businesses and raised water rates.

Such revenue sources are limited, however, and the next mayor - to be chosen at a special election within six months - probably will face the tough choice of raising property taxes or resoring to the deficit financing that has hurt the credit of other cities.

"People will blame him (the new mayor), and attribute the problem to Daley's death," a top officer of a large financial institution predicted. "But the truth is that the petroleums have been growing," he said.

Daley enjoyed vast power - he was more powerful than the govenor or senators - because, in addition to being mayor, he was Democratic chairman of Cook County. For more than two decades in the dual role Daley controlled the nation's most powerful political machine, with some 15,000 patronage workers whose most important job qualification was the ability to deliver the popular vote.

He enjoyed a broad base of support both from labor and the predominantly Republican business establishment - an alliance that his death has shaken.

Ben W. Heineman, chairman of Northwest Industries, a Chicago conglomerate, says there is "a significant risk" that the next mayor won't be strong enough to resist adopting policies that are politically popular but financially unsound."

Heineman said: "Daley was unique in his ability to deal directly and effectively with both Labor and business, and he was strong because he held both the mayoral and political power."

THat power, according to attorney Polikoff, made Daley perhaps the only municipal executive in the country who could have dealth effectively with the problems of schools, housing and unemployment. But Daley didn't seize the opportunity, Polikoff said.

"Daley's city was subject tot he sam forces that have overwhelmed Detroit, Cleveland, and St. Louis," Polikoff said. "Maybe the forces would have overwhelmed even Daley, but the one thing you can say is that he never tried."

Polikoff went on: "The city works or doesn't work depending on who you are. It works for the affluent who live in high-priced housing areas. Not only has it not worked for those who are not affluent, it has been a disaster."