Chicago, a city notoriously unreceptive to new ideas, is in agony.

During the 1968 Democratic National Convention, its police, who never had seen such a thing before, literally beat a peace protest into the ground. Mayor Richard J. Daley averred that they were about to poison the water supply.

A majority of its citizens appeared to agree that this was the proper way to deal with a historic first.

Now Chicago is being torn apart by a choice between two unthinkable political novelties. It must have either the first black mayor in its history, or the first Republican in half a century.

Neither of the candidates who are vying to break the mold is making it the least bit easier for the voters. Sometimes they seem to be competing for an unattractiveness trophy.

Rep. Harold Washington (D-Ill.), an able former state legislator who was twice elected to the House, was the surprise winner of the Democratic mayoral primary, benefiting from the split that developed between incumbent Mayor Jane M. Byrne and challenger Richard M. Daley, heir-apparent of the late mayor.

Bernard Epton is 61, a liberal, a Republican, who two months ago was wandering lonely as a cloud on the fringes of a gala fund-raising banquet, which Sen. Charles H. Percy (R-Ill.) staged for himself and which President Reagan addressed. Epton querulously importuned visiting reporters to note that not only was he not seated at the head table but that none of the numerous speakers of the evening had so much as mentioned his name.

Now Epton is the great white hope of Chicago's ethnic voters, who see in a Washington victory a threat to their way of life.

The election has become a minefield, through which the two principals walk with rock-heavy tread.

Obscene campaign buttons are worn proudly by people who make no secret of or apology for their bigotry. Ugly scenes occur in churches.

The candidates make intemperate statements. Washington is howled out of white neighborhoods; Epton dares not go among the blacks.

The world's press attends the ugly rites. Both Washington and Epton have acquired high-powered national media consultants. Pat Caddell, oft-time pollster to Democratic presidential candidates, joylessly coaches Washington, trying to keep him from pouring more gasoline on the flames.

John Deardourff, the moderate Republican ace, is wearing Epton's livery, and attempting to get him to talk about something other than Washington's admittedly lamentable record as a taxpayer.

Neither consultant seems smitten by the championship caliber of his horse.

"Washington is no Andy Young," mourned Caddell, speaking of his glowering, impolitic contender.

"Bernie is inexperienced," sighed Deardourff of the testy, impolitic Epton.

Washington, obviously wanting to keep his contituency at the proper edge for election day, has expressed the happy thought that if he is cheated of his prize by racism "some innocent person walking down the street may end up dead."

Epton, who has an unblemished civil rights record and professes to reject racist support, nonetheless fights under the slogan, "Before it's too late"--which is widely interpreted to be a warning to whites to shake a leg or wake up with vengeful hordes swarming over City Hall.

The road to the present state of affairs is marked with "if onlys."

If only, obviously, on primary night Washington had proclaimed his upset win as a victory for the whole city and not just its black voters. If only he had held a hand out to the shaken and resentful precinct captains, the machine might have closed its eyes to his transgressions--as would have been the case if he were of a different color--and set about electing him in the usual way.

But he didn't. With an exultant Jesse Jackson, one of Chicago's less reassuring figures by his side, Washington emitted the battle cry, "Now it's our turn!"

Similarly, had Epton paused in his denunciations of Washington as a crook, unfurled some kind of a vision of the city, indicated some leadership traits on the trail, he might have rallied the guilt-free white liberals who are choking on Washington's record.

Washington served a month in jail for avoiding income taxes for four years, although he is, according to his biography in the Congressional Record, founder and president of the Black Taxpayers League--and was born, in 1922, on April 15, tax day.

He was suspended from practicing law for having taken money from indigent clients and having failed to render services.

He said of his deadbeat past that he has "paid his dues," and explained that he always has paid his bills slowly.

Chicago was a closed city under the long, hard rule of Daley. It was not a system in which new ideas and political talents flourished. Willy-nilly now, it's going to be opened up in ways its citizens never imagined.