First Chicago Corp., which owns that city's second-biggest bank, has announced plans to buy Chicago's fifth-largest bank for $275 million from Walter E. Heller Corp.

First Chicago Chairman Barry Sullivan said this week that Heller's American National Bank will be operated as a separate subsidiary of First Chicago.

American National is the last important asset owned by Heller, once a major factor in U.S. industrial finance. Heller sold its domestic and international finance subsidiaries to Japan's Fuji bank last March. If regulators approve the sale to First Chicago, Heller will be liquidated.

First Chicago had assets of about $35 billion on June 30. Even with the addition of American National's $3 billion in assets, First Chicago will still be smaller than Continental Illinois National Bank, which has $41 billion in assets.

But the once agressive Continental has been reeling for the last year as a result of more than $1 billion loans it purchased from the now-defunct Penn Square National Bank of Oklahoma City. Most of those loans have either gone sour or are on Continental's problem list.

Meanwhile, First Chicago, which was in deep trouble seven years ago, has been moving confidently for the last year to become, in chairman Sullivan's words, the premier bank in the Midwest.

Sullivan said that American National is a highly successful lender to Chicago's middle market--companies with annual sales from $5 million to $115 million--where First Chicago is not as strong as it would like to be.

Sullivan said he did not think the federal government would have any antitrust objections to the acquisition. He said he also did not think it would hurt First Chicago's bid to buy financially distressed First Federal Savings & Loan Association of Chicago.

First Federal has been kept afloat by subsidies from the Federal Home Loan Bank Board. Sullivan said First Chicago would drop its bid to buy the thrift institution if it appeared the acquisition would endanger its proposed purchase of American National.

First Chicago had profits of $86.5 million last year, while American National earned $12.3 million. First Chicago is a major multinational bank, with global operations. American National, on the other hand, is mainly a Chicago area bank.