By Anthony Esposito

SANTIAGO, Nov 17 (Reuters) - As Chileans head to voting booths on Sunday to pick who will lead the country for the next four years, the biggest question mark is whether former President Michelle Bachelet wins outright or needs to wait for a December runoff.

The center-left Bachelet has promised to narrow the worst income inequality among the 34 member states of the Organization for Economic Co-Operation and Development by leveling the playing field in education. She has also pledged to upend a constitution that dates back to Augusto Pinochet's 17-year dictatorship.

Her Nueva Mayoria (New Majority) coalition, which spans the political spectrum from communists to moderate Christian Democrats, must also win big in congressional elections on Sunday in order to muster the political might needed to implement those changes.

"In order to confront inequality, I invite you to vote en masse for the Nueva Mayoria this Sunday. We want to win in the first round because we have a lot of work to do," Bachelet told a packed crowd at her campaign's closing ceremony on Thursday.

Trailing a distant second to the 62-year-old Bachelet in the polls is Evelyn Matthei, 60, the candidate for the governing right-wing Alianza coalition.

A candidate winning over half the votes would be elected outright - something that has not happened in 20 years. Otherwise, the two top contenders will go head to head on Dec. 15.

One recent poll of likely voters suggested Bachelet may get the votes she needs for a first-round victory.

But other polls have shown that support for the eight other candidates, including Matthei, maverick economist Franco Parisi and former socialist congressman Marco Enriquez-Ominami, could fracture the vote and push Bachelet into a second round against Matthei.

In any case, pollsters and political analysts believe Bachelet would easily win a runoff against Matthei. Bachelet, who held the presidency from 2006 to 2010, was constitutionally barred from seeking immediate re-election after her first term, but left office enjoying stratospheric popularity.

The Andean country, the world's top copper producer, moved to a voluntary voting system from a compulsory one last year, injecting a dose of uncertainty into electoral forecasts.

All 120 lower house seats and 20 out of 38 Senate seats are also being contested on Sunday. Under the Chilean system, the governing coalition needs more than a simple majority to pass some kinds of legislation, making it easier for the opposition to block key reforms - a Pinochet-era legacy that Bachelet wants to change.