Goodwin Chase, chairman of the Renegotiation Board, has resigned, leaving the small federal agency which guards against profiteering on defense contracts incapable of any official action -- perhaps permanently.

Chase's resignation follows two stormy years in the post and leaves the board with two members and three vacancies. The board needs a quorum of at least three voting members to act on any of its cases.

Normally, the deficiency could be corrected by a presidential appointment to fill at least one of the vacancies. But the board's status is not normal; the 27-year-old agency is scheduled to go out of existence on March 31.

Thus, even if President Carter does nominate a new board member, the Senate confirmation process could probably not be completed before the board's life expires.

The Renegotiation Board reviews defense and space contracts to determine whether a contractor's profit is excessive. If such a determination is made, the board can order the firm to pay back some of its earnings.

In fiscal 1978, the board ordered 37 firms to pay the government a total of $31.5 million.

The defense industry lobbied hard in Congress last year for legislation to abolish the watchdog agency, and both houses agreed to kill the agency as of March 31.

In his budge message to Congress last week, Carter asked for additional funding to keep the board operating for at least two more years. But both friends and foes of the agency in Congress say it is doubtful that any action will be taken before the March 31 deadline.