PARIS, JAN. 16 -- Prime Minister Jacques Chirac, declaring himself "ambitious for France," today became the first of France's major political contenders to announce formally his candidacy for president.

Chirac's brief televised announcement, which had been expected for months, constituted the official opening shot in a three-month political battle leading to presidential elections set for April 24 and May 8.

Chirac, leader of the neo-Gaullist Rally for the Republic party, has been prime minister since March 1986 at the head of a conservative coalition that has sought to reverse nationalizations and other measures instituted by a Socialist government from 1981 to 1986. In so doing, he has been the main actor in France's so far successful experiment called cohabitation, matching a Socialist president with a conservative government and parliamentary majority.

Chirac's chief opponents in the presidential race are expected to be former prime minister Raymond Barre, a member of the governing coalition but without a formal party, and President Francois Mitterrand, the popular Socialist patriarch elected in 1981 for a seven-year-term as chief of state.

Chirac's problems at the outset of the campaign were underlined by an opinion poll that appeared today showing Barre or Mitterrand as more likely winners in the two-round election. Although regarded as a fierce campaigner of limitless energy and consummate skill, Chirac's consistent ratings in opinion polls placing him behind Barre or Mitterrand have become a major obstacle to his aspirations.

The latest poll, sponsored by the newspaper Liberation and the private television channel TF1, showed 41 percent of voters favoring Mitterrand, 25 percent for Barre and 18.5 percent favoring Chirac. In his first presidential candidacy in 1981, Chirac won 18 percent of the vote.

Equally discouraging for the Chirac camp, today's poll showed that if the election were held now Mitterrand would be the victor against Chirac, 54 percent to 37, with 9 percent of those questioned not giving an opinion. He would be the victor against Barre, 49 percent to 43, with 8 percent not giving an opinion.

Chirac's aides have said the ratings will change, however, as Barre and Mitterrand are forced to grapple with issues more frequently in the heat of campaigning and as the Gaullist political machinery goes into action across France.

French analysts said Barre, an economics professor who seeks to maintain a distance from day-to-day politics, plans to make a formal announcement of his candidacy later this month. But Mitterrand, who the polls repeatedly have said could triumph over either of the two conservative contenders, has refused to confirm whether he will run for reelection as is increasingly expected.

This tactic, allowing him to benefit from the dignity of his office, has irritated Chirac and Barre, leading both to make oblique criticisms of Mitterrand's coyness only 98 days before the first round of voting. Unless Mitterrand decides not to run, analysts have said it is almost certain that the first round April 24 will eliminate either Chirac or Barre on the right and send the best placed of the two against Mitterrand in the runoff around May 8.

Two former Socialist ministers, Michel Rocard and Jean-Pierre Chevenement, also have expressed presidential ambitions from the left. But Mitterrand has gained such popularity as president that his entry into the race would in effect eclipse their hopes barring a major shift in public opinion.

A top presidential aide said this week that Mitterrand genuinely has not made up his mind. At 71, the president's supporters have said, he is torn between the desire to reflect or write as an elder statesman and the fear that his Socialist Party would lose its recently acquired place on the French political scene if a less popular candidate took up the banner.

The aide conceded that Elysee Palace officials have begun work on campaign planning. In addition, several Mitterrand supporters have organized fund-raising networks with no sign from the president that they should halt their efforts.

Chirac, 55, who started his political career as a favorite of president Georges Pompidou in the 1960s, has gained a reputation among friends and foes as a tireless worker and a master of political maneuvering. Although he has become known for personal kindness -- adopting a Vietnamese refugee, for example, or dropping state business to arrange a friend's eye operation -- he has failed to create an image of himself as a man with constant principles or long-term vision.