First Chicago Corp., parent of the troubled First National Bank of Chicago, announced today that Chase Manhattan Corp. Executive Vice President Barry F. Sulliavan will become chairman on July 28.

First Chicago, saddled with the highest percentage of bad loans of the nation's major money center banks, also said it had "reached an understanding with the comptroller of the currency" to hire a management consulting firm to study the banks operations and carry out reforms based on the firm's suggestions.

Although First Chicago is not in financial danger, as was First Pennsylvania Corp. before it was bailed out by other banks and the federal government several months ago, the bank's earnings have been sliding and its executive ranks have been riddled, in large part because of the abrasive five-year tenure of the bank's former chairman A. Robert Abboud.

Abboud was forced out as chairman of the nation's ninth-biggest bank in April after a policy dispute with his newly appointed president triggered a board re-examination of Abboud's performance.

Abboud stayed on as chairman until a successor was found. The president, Harvey Kapnick, was fired immediately.

Ben W. Heineman, who effectively has run First Chicago since April as chairman of its executive committee, said today that a consulting firm, A. T. Kearney, also will study the management of the bank and recommend change in structure and personnel as well.

Sullivan, 49, has been with Chase for 23 years and has been a member of its seven-person management committee since 1974. Since 1978 he has been responsible for Chase's corporate and international banking, as well as merchant banking and information services.

He will inherit a big (deposits of $21.1 billion at the end of 1979) but dispirited institution which has spent most of the five years Abboud headed it trying to rid itself of loan problems that began in the late 1960s and early 1970s during the tenure of Gaylord Freeman, Abboud's predecessor who hand-picked Abboud for the job.

Although Abboud succeeded in halving the percentage of "nonperforming loans" in First Chicago's portfolio, he did so in a way that not only drove out many of the bank's brightest officers, but also alienated some of the bank's best customers

"There are very serious, deep-seated problems at that bank," said one big bank official who knows First Chicago well. "Sullivan faces one of the meanest jobs in banking."

The consulting firm will focus on a number of areas at First Chicago, including the bank's management of funds, the adequacy of its capital, its loan exposure in foreign countries (called country risk), its commercial lending practices and its foreign exchange operations.

What worries bank analysts and regulators about First Chicago is the high level of bad loans (called nonaccruing assets) on its books.

A Salomon Brothers study said that at the end of 1979 nearly 3 percent of First Chicago's loans were not producing. "That's as big as Bankers Trust and Chemical (two New York banks) combined and neither of them are roses," said a well-placed banking source.

As the recession begins to take hold, banks are bracing for a significant increase in the number of loans on their books which will go sour -- at least temporarily.Because First already has so many bad loans -- a chunk of them real estate loans -- some analysts fear the bank's situation could get markedly worse before it gets better.