Assistant Secretary of State Patsy T. Mink and two other women yesterday filed suit against the University of Chicago and a leading pharmaceutical maker, charging that during pregnancy they were given, without their knowledge, a drug now linked to cancer in offspring.

They asked $77.7 million in damages on behalf of themselves and nearly 1,100 other women who were given the drug DES in an experiment. The experiment, conducted in 1951 and 1952, was designed to find out if DES would prevent miscarriage.

In 1971, 20 years after the experiment at the university's Chicago Lying-In Hospital, scientists discovered that rare and sometimes fatal vaginal or cervical cancer developed after puberty in the daughters of a small proportion of the estimated 1 million or more women who had taken DES pills during the first trimester of pregnancy. The number of documented cases of DES-linked vaginal cancer is about 120.

More recently, scientists published evidence that sterility or other abnormalities of the reproductive tract may-occur in some sons of women who had taken the pills in early pregnancy. In addition, most DES daughters have vaginal adenosis, an apparently begin but in some cases perhaps precancerous abnormal cellular formation of the cervix.

Although there is no proof to this day that DES (diethylstilbestrol) prevents threatened miscarriage, physicians have been prescribing it for this purposes for about 30 years. They have continued to write thousands of prescriptions for it annually even since Dr. Arthur L. Herbst and his associates at Massachusetts General Hospital reported six years ago their discovery of vaginal cancer in DES daughters. Since then, the Food and Drug Administration repeatedly has warned doctors about the danger and ineffectiveness of DES, an estrogen.

Mink and the other two plaintiffs - each with a daughter born at Lying-In between July 5, 1951, and March 6, 1952 - filed the suit in U.S. District Court in Chicago. They sued on behalf of themselves and 1,078 women who were given DES pills in the experiment, conducted by the late Dr. William Dieckmann over a 20-month period ending Nov. 20, 1952.

Mink and the other plaintiffs in the class action, Phyllis S. Wetherill of the District of Columbia and Gladys E. Lang of Stonybrook, N.Y., alleged that while receiving prenatal care at university clinics, they were given and directed to take DES while 1,081 other women were given dummy pills. The pills were distributed randomly without regard to medical needs, according to the complaint.

None of the women was advised that she was participating in an experiment, the complaint said. Mink and Wetherill each charged that she was told she was getting "vitamin pills." Lang said she was told the pills would help to prevent complications in pregnancy, although, the complaint said, "Diekmann personally believed that-prior studies had not shown DES to be effective during pregnancy for any medical purpose." Unlike the others, his study was carefully designed to eliminate bias.

The plaintiffs, represented by lawyers for the Health Research Group, a Washington-based unit of Ralph Nader's Public Citizen, Inc., named as codefendant Eli Lilly & Co., the Indianapolis-based firm that supplied DES pills for the study and provided one of is own employees to Dieckmann.

The class-action lawsuit seeks $70,000 in damages to compensate each of the 1,081 women who got DES, mainly for the hazards created for their children and for "severe mental anxiety and emotional distress." Each of the three plaintiff's daughters have vaginal adenosis.

The suit also seeks punitive damages of $2 million, accusing the university and the company of "intentionally concealing from plaintiffs that they had been given DES and breaching their duty to inform plaintiffs and their children of the experiment and of the precautions which their children . . . should take to minimize the risk of their contracting cancer or other abnormalities."

In a preliminary comment made before seeing the complaint, university vice president Don Bruckner told a reporter that as a result of Dieckmann's experiment, university doctors immediately stopped using DES and urged physicians elsewhere to do the same. The Lilly firm had no immediate comment.

The FDA ordered DES makers in November, 1971, to stop making and promoting if for prevention of miscarriage. The medical community generally recognized by 1973 that DES daughters should have certain semi-annual checkups.

But the Lilly firm "has never notified" Mink, Wetherill or Lang that each had received DES in an experiment that the company had "participated in, encouraged, and approved," and on which the university kept records, the complaint said.

The complaint included a form letter from Lying-In Hospital notifying recipients that they had received DES in the experiment and urging their sons or daughters to come in for a free check-up under a National Institutes of Health research grant.

Mink's copy, dated Jan. 29, 1976, reached the former congresswoman in Honolulu on March 5, 1976. Wetherill's letter was dated Dec. 5, 1975, and Lang's Aug. 28, 1975.

The letters "did not disclose that the drug had been administered without the plaintiff's knowledge . . . nor did they inform plaintiffs of the precautions that their daughters should take," the complaint said.

In Detroit last month, a judge took under advisement the question whether 153 DES mothers could sue Lilly and other manufacturers.