Chase Manhattan Mortgage & Realty Trust, once the fastest growing firm in the nation's fastest growing industry, today filed for bankruptcy in federal court here.

The real estate investment trust, which bore the name of the country's best known bank, had been in serious trouble, like many other investment trusts, since 1974 when the construction industry went into a deep tailspin leaving Chase with many defaulted mortgages and a long list of banks to which it owed money.

For the last four years Chase has been gradually reducing its debt, selling off many of the properties it acquired when it foreclosed on bankrupt builders and otherwise making peace with its bank creditors.

Once the Chase investment trust -- the Chase Manhattan bank served as management adviser to the firm and is a major lender to it but does not own the firm -- had assets of more than a billion. Today its assets have shrunk to $270 million.

The investment trust's latest troubles began last May when it defaulted on payment of $36.7 million in notes sold in 1971.

It has since announced plans to restructure its debt including paying holders of the defaulted notes 90 cents on the dollar without interest plus 7 shares of convertible preferred stock for each $1,000 worth of notes.

Under the bankruptcy petition filed today, the real estate investment trust asked the court to protect it against law suits from creditors while it works out a plan to pay off those to whom it owes money.

As part of the proposed debt restructures Chase Manhattan bank would loan the real estate investment trust $20 million.

Real estate investment trusts grew from almost nothing in 1968 to a $21 billion industry in 1974, capitalizing on the boom that occurred in the building industry.

The trusts' profits were tax free as long as 90 percent of the earnings were passed along as dividends to the investors.

Most of the loans were made to builders of condominiums, shopping centers and the like. Because the trusts had to pass along most of the profits to shareholders, nearly all the funds they lent out had to be borrowed from someone else.

Eventhough the interest rates the investment trusts charged were high, soaring real estate values, relatively scarce mortgage money and a giddy desire to build made the trusts popular sources of money for builders.

But all booms come to an end, and when the construction industry collapsed, starting in 1974, many developers went bankrupt. Hoping for a revival in building, many real estate investment trusts were at first relunctant to foreclose on the builders and take possession of the properties.

But many trusts, including Chase, were left without enough cash flow to pay off their creditors, mainly big banks. The banks, which had billions of dollars mainly in big loans to the trusts, were patient. They rescheduled debts, and took possession of foreclosed properties in return for writing off some loans.

Chase Manhattan Realty Trust went through several debt restructurings, but finally ran out of cash when the notes came due last May.

Under the plan presented to the court today the 27 big banks -- including such names as Chase Manhattan, Chemical Bank, Manufacturers Hanover, First Pennsylvania and Crocker -- would receive assets or cash equal to the $150 million they are owed.

The public holders of the notes would receive 90 percent of the money they are owed plus the new shares of preferred stocks.

Owners of $71.7 million in notes and debentures who have lower priority than the banks and the 1978 noteholders, would get about 40 percent of what they are owed -- 15 to 20 percent in cash plus new shares of stock.

What would be left, the plan contemplates, is a virtually debt-free company worth about $46 million, owned in the main, by virtue of the new stock offerings, by those who once loaned the company money.