Virginia State Sen. John H. Chichester of Fredericksburg today became the second candidate to announce formally for the Republican nomination for lieutenant governor, acknowledging that he is starting out behind former state attorney general J. Marshall Coleman of McLean.

Chichester, elected to the Senate in 1978, said he has less name recognition than Coleman, the party's 1981 candidate for governor, but said he expects to gain party support at the GOP convention May 31.

Chichester, 47, owner of an insurance agency, has never run for statewide office. "I am eager to help lead the Virginia Republican Party to its rightful place as majority party in the Old Dominion," he said.

In comments to reporters after his announcement at the state GOP headquarters here, he declined to criticize Coleman directly.

But Chichester said he would reject "divide and conquer" leadership, an indirect reference to Coleman's unpopularity with some party leaders and Coleman's come-from-behind nomination for attorney general in 1977.

"He's a nice fellow, I have no criticism of him," Coleman said later. "We have surveyed the rank and file . . . . Someone who is not simply a regional candidate can go a long way in determining whether we win or lose. I'm going to focus my attention not on Republicans but on the Democrats and why we ought to evict them."

Other potential Republican candidates are state Del. A.R. (Pete) Geisen of Augusta County, chairman of the joint House-Senate Republican caucus, who has scheduled a Dec. 18 news conference to enter the race, and Maurice Dawkins, a Washington lobbyist who lives in Springfield.

Falls Church direct-mail king Richard Viguerie has expressed an interest in running. Viguerie, who has never sought public office, is considered a wild card in the contest. Another frequently mentioned candidate, state Del. Frank D. Hargrove of Hanover County, has decided not to run and has endorsed Chichester.

In his speech, Chichester pledged a largely conservative agenda, lashing out at a "philosophy of leniency" that has led to the state's "coddling of criminals."

He specifically criticized a state agreement with the American Civil Liberties Union over operation of the troubled Mecklenburg prison, saying Virginians want a government "that will not acquiesce to the ACLU and other pressure groups."

Chichester is known for his 1980 refusal to vote on the Equal Rights Amendment when it was before the state Senate. Chichester's abstention -- he opposed the bill -- avoided a 20-20 vote that would have thrown the issue to then Lt. Gov. Charles S. Robb, who was an ERA supporter. The measure needed 21 votes.

Chichester said yesterday he has the support of GOP congressmen Thomas J. Bliley Jr. of Richmond and Herbert T. Bateman of Newport News and of Rep.-elect D. French Slaughter, of the 7th District, which includes Fredericksburg.

Northern Virginia supporters include Fairfax Dels. Stephen E. Gordy, Robert E. Harris and Frank Medico and State Sen. John W. Russell of Fairfax City.