The United States yesterday turned over to the Israeli government for trial an alleged Palestinian terrorist who has been fighting extradition from this country and protesting his innocence for 2 1/2 years.

U.S. authorities in Chicago surrendered 21-year-old Ziad Abu Eain to Israeli officials after Deputy Secretary of State William P. Clark signed a surrender warrant.

Abu Eain was taken from Chicago to New York where he was to be turned over to Israeli custody last night for a flight to Tel Aviv expected to arrive at noon today.

It is the first extradition request since Israel and the United States signed an extradition treaty in December, 1963.

"I have concluded that our treaty with Israel and compelling law require a conclusion that Abu Eain be extradited," Clark said in a written statement.

Clark also said he rejected arguments by Abu Eain and his supporters that the Palestinian could not get a fair trial in Israel "within a judicial system not unlike our own system."

"We have been formally assured by the government of Israel that the crimes charged against Abu Eain--murder, attempted murder and causing bodily harm, with aggravating intent--are common criminal charges which will be tried in an ordinary civilian court . . . ," Clark said.

"I do not and need not for purposes of extradition make any decision on the question of Abu Eain's guilt or innocence," Clark said. "That determination can be made only by a trial court."

Supporters of Abu Eain, who made him a rallying point for the Arab American community in this country, took his case to the Supreme Court in their effort to keep him from Israeli custody. However, last September, the high court refused to consider the case, leaving it in the hands of the State Department, where Abu Eain had petitioned for assistance.

The Israeli government sought Abu Eain for allegedly participating in a May, 1979, bombing by the Palestine Liberation Organization.

Abu Eain's supporters here reacted to the extradition with outrage.

Jim Zogby, executive director of the American-Arab Antidiscrimination Committee, condemned the State Department decision as "clear evidence of discrimination in this country against Arabs" and a "clear indication at the Department of State of the total insensitivity that the department has toward people of Arab descent."

He said that the department had set up a meeting for Thursday with Clark and ambassadors of four Arab countries on the Abu Eain case. "They the ambassadors have indicated very clearly, at the highest levels, that this is an extremely serious case in the Arab world," Zogby said. "They have slapped the Arabs in the face and they are asking for an Arab response," he said of the State Department.

"It was our fear," he added, "that he would not receive justice in this country because the requesting party was Israel. There's the presumption of guilt because the requesting party is Israel."

In his statement, Clark recounted the details of a statement given to Israeli interrogators by Jamal Hasan Ahmad Yasin, who was a friend of Abu Eain and who said he gave Abu Eain a bomb and timing mechanism on May 14, 1979.

The bomb was placed in a refuse bin in the marketplace of Tiberias, according to Yasin. The next day, Yasin said, he met with Abu Eain and told him of news reports of a bomb explosion in the marketplace. Yasin's statement said that "the operation had succeeded, that two persons had been killed and 36 injured."

Supporters of Abu Eain have strongly attacked the veracity of Yasin's statement, which has been the basis of court rulings in favor of Abu Eain's extradition to Israel.

After the May, 1979, bombing, Abu Eain ended up in Amman, Jordan, and on June 14 that year flew to Chicago, where he took up residence with his sister and her husband. In July, he was picked up by FBI agents and jailed pending the extradition proceedings.