SANTIAGO, Chile - Presidential hopeful Soledad Alvear bowed out of the ruling center-left coalition's primary race, saying on Thursday she would back Socialist Party candidate Michelle Bachelet to become Chile's first woman leader.

The decision makes Bachelet, briefly imprisoned after a 1973 military coup that launched the Augusto Pinochet dictatorship, an increasingly clear favorite to win December's presidential election, according to opinion polls.

Alvear, a former cabinet minister who ran an uninspiring campaign, made her announcement 10 days after Chile's right wing coalition, which has been in the opposition for 15 years, surprisingly split in two.

The race is now three ways between Bachelet, a Socialist Party-mate of popular President Ricardo Lagos; conservative Joaquin Lavin, struggling to distance himself from the legacy of Pinochet; and newly declared center-right businessman Sebastian Pinera.

"This way Michelle Bachelet becomes the only candidate of the (center-left coalition) Concertacion and the future president of Chile," Christian Democrat Alvear said at a press conference.

An opinion poll last week showed 44.0 percent support for Bachelet, 20.9 percent for Lavin, 16.4 percent for Pinera and just 9.1 percent for Alvear.

Political scientist Patricio Navia of Diego Portales University said to win Alvear supporters Bachelet must adopt some of her issues- such as family values and small business support- and bring bosses from Alvear's Christian Democrat party to her campaign team of Socialists.

Bachelet, a former defense minister and health minister, has been cautious about spelling out policies but has won support through her charisma and personal history.

She went into exile after the coup and her father died after being imprisoned and tortured.

Since ex-Senator Pinera has just joined the race it is not yet clear whether he or Lavin will be pressured out before the election.

"Neither of the rightist candidates has a clear advantage, and as long as that is the case it is hard for one of them to step down," Navia said.