Chase Manhattan Corp., which controls the nation's third-biggest bank, said last week it had filed for permission to open a bank in Delaware to take advantage of that state's lower taxes and lack of ceilings on consumer interest rates.

Chase has joined a small group of New York banks which have set up operations outside that state, or plan to, in order to avoid usury ceilings on interest rates (which New York raised sharply last year to keep banks from leaving) or to lessen their tax burden or both.

In an attempt to woo major banks, Delaware last year passed a law permitting bank holding companies to set up new banks in the state. Delaware has no usury ceilings.

Early last year South Dakota took a similar step to lure Citicorp, which controls New York's biggest bank, to Sioux Falls. Last February Citibank South Dakota opened, and the bank gradually is transferring its Vista and MasterCard accounts to the South Dakota bank.

Three weeks ago, the parent company of Morgan Guaranty Trust Co. filed an application with federal regulators and the State of Delaware for permission to open up a subsidiary bank. Morgan has limited consumer banking services and wants to run primarily what is called a "wholesale" banking operation aimed at businesses, governments and institutions.

A spokesman for Chase said the Delaware bank would be called Chase Manhattan Bank, U.S.A. Many of Chase Manhattan's credit card operations and consumer installment loans, such as student loans, would be located in the Delaware subsidiary.

Although Chase seeks to avoid usury limitations in addition to paying lower taxes, a Morgan spokesman said that bank is making its move mainly because of the tax climate in Delaware.

Chase said today that it filed an application with the Comptroller of the Currency, which regulates federally chartered banks, and would file in Delaware shortly. A spokesman said the bank hopes to have the subsidiary bank in operation this year or early next year.

John Malarkey, banking commissioner of Delaware, said it is too early to determine how many banks will take steps similar to Chase's or Morgan's. He said other states may pass laws similar to Delaware's to keep banks from setting up out-of-state operations.