By Simon Gardner

SANTIAGO, Oct 27 (Reuters) - Chile's rightist parties came out from the shadow of former dictator Gen. Augusto Pinochet in local elections at the weekend, boosting their hopes of wresting power from a weakened center-left government next year.

President Michelle Bachelet's center-left coalition, the Concertacion, won the most council seats in Sunday's municipal elections, but the center-right Alianza coalition dominated in mayoral posts.

Early polls tip a center-right billionaire to win the 2009 presidential vote, although analysts say the two coalitions that dominate Chilean politics will both need to forge alliances with centrist independents and it will be a close race.

"In political terms, it is an important triumph for the Alianza, because it won emblematic bastions and major cities across the country," Marta Lagos of polling firm MORI in Santiago said of Sunday's election results.

"But in terms of numbers, it is not a triumph that secures it the presidency."

The center-left Concertacion has ruled Chile since the end of Pinochet's 1973-1990 dictatorship, leading the country in a long period of economic growth and political stability.

But its appeal has faded in recent years amid infighting in the governing coalition, and many voters feel it has failed to deliver.

Bachelet's popularity rating has taken a beating in recent months, rocked by anger at a botched revamp of the capital's bus system, sometimes violent protests by students against education reform and worries about crime and annual inflation running at around 9 percent -- its highest level since 1994.

The president now plans to shuffle her cabinet as her embattled coalition faces its toughest presidential race in two decades. She is not allowed under Chile's constitution to seek re-election and the Concertacion has not yet picked its presidential candidate.

Any serving minister who wants to run for political office in next year's presidential and congressional elections must leave their post by mid-December, a year ahead of the vote.

The local elections on Sunday showed the Alianza gaining ground, although few doubt it will be a hard-fought presidential race.

Alianza won around 40 percent of the tally for mayors, including central Santiago, against around 38 percent for the ruling coalition. There were 345 mayoral posts up for grabs.

However, Concertacion won around 45 percent of the vote for 2,160 local councilor posts, against Alianza's 36 percent.

"The people yesterday expressed an opinion deeper than their vote, and in a way made clear it wants more unity," said Bachelet. "The people don't want to see any more fighting, they want to see their leaders working."

Alianza's center-right billionaire Sebastian Pinera has long distanced himself from Pinochet, who died in December 2006 before facing a full trial for abuses committed during his rule, when around 3,000 people were killed and another 28,000 were tortured -- most of them suspected leftists.

But Pinochet's shadow has not disappeared completely.

The late dictator's eldest daughter, Lucia Pinochet Hiriart, won a council seat in the luxurious Santiago neighborhood of Vitacura running as an independent. (With reporting by Rodrigo Martinez; Editing by Kieran Murray)

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