* Center-left Bachelet promises tax, education reform
* In Chile first, two women are president front-runners
* Matthei, Bachelet have known each other since childhood (Adds voters' quotes)
By Alexandra Ulmer
SANTIAGO, Dec 15 (Reuters) - Chileans were voting on Sunday in a runoff election likely to hand former President Michelle Bachelet a fresh four-year term, with the center-left leader gunning for a landslide triumph to bolster her reform mandate.
In Chile's first presidential showdown between two women, voters are expected to give overwhelming backing to Bachelet, who led the country from 2006 to 2010, impressed by her easy charm and plans to tackle deep income inequality.
Her right-wing rival, the sharp-tongued Evelyn Matthei, has been weakened by her family's ties to the 1973-1990 military dictatorship of General Augusto Pinochet and by her post in the unpopular government of outgoing President Sebastian Pinera.
In the first round of voting on Nov. 17, Bachelet, a 62-year-old pediatrician by training, won nearly twice as many votes as Matthei, a 60-year-old economist and former labor minister. But Bachelet fell just short of the 50 percent needed to win outright, pushing the vote into a runoff.
The two women were playmates during their childhood on an air force base, though the bloody 1973 military coup later divided their families.
"This is not about choosing between 'two women', as the press likes to put it," Bachelet said in a closing campaign speech to hundreds of cheering supporters on Thursday.
"There are deep differences here. I think Chile is ready to face the transformations that will allow it to be the country we all want. We can turn Chile into a truly developed country."
Robust, copper-led economic growth has turned Chile into a Wall Street favorite, but many Chileans feel they have yet to see the fruits of the mining boom as wealth and power remain largely concentrated in the hands of a small elite.
Bachelet wants to hike corporate taxes to pay for a wide-ranging education reform, shred the dictatorship-era constitution, and legalize abortion under certain circumstances.
"I voted for Bachelet. I want changes for the people, for young students, more opportunities for those of us who are lower-middle class," said Maximiliano Valdes, a 25-year-old electrician. "The changes she's promised can be done."
There have been no major polls ahead of the run-off, mainly because Bachelet's victory has been taken for granted.
While there is little doubt about the overall outcome, analysts say this assumption could result in voter apathy and low turnout that could deny Bachelet the dramatic win she is looking for to pressure a notoriously tricky Congress to approve her reforms. Disillusion with politicians also runs high.
"Bachelet doesn't convince me. Neither of the two candidates convinces me," said Raquel Baeza, a 37-year-old accountant who didn't vote, preferring to go Christmas shopping in the center of Santiago. "I'm left-leaning, but I would have liked someone other than Bachelet. She just creates a committee to think about what to do, she doesn't do anything concrete."
Both candidates voted early on Sunday, likely to encourage their compatriots to do the same amid the Southern Hemisphere's December heat.
Bachelet was greeted by throngs of supporters, who leapt forward to kiss and photograph her. Matthei, on the other hand, had to deal with a small group of protesters, apparently demonstrating against the installation of a factory in their community.
"My main call is for participation," Bachelet said after she cast her ballot. "With skepticism we can't produce the changes we need."
Bachelet and Matthei were neighbors during their childhood on a base in northern Chile, where their fathers were air force generals who became close friends.
The girls rode bikes and played together in the street, according to a bestselling book about them.
But the military coup that ushered in the 17-year long Pinochet dictatorship affected them very differently.
Matthei's father became a key member of Pinochet's junta while Bachelet's father, loyal to deposed socialist President Salvador Allende, was arrested, tortured by Pinochet's agents and died in prison.
Bachelet and her mother were also tortured before fleeing into exile.
Matthei backed Pinochet in a 1988 plebiscite about his rule, a decision that has dogged her in this election campaign just as Chile commemorated the 40th anniversary of the coup.
In her closing campaign event on Thursday, Matthei linked Bachelet's reform drive to the far-left government of Venezuela.
"They want to change the constitution to resemble Venezuela, where every day it's harder to find food," Matthei said. "Does that remind you of anything?," she added, in an apparent reference to shortages of the Allende era.
She and Bachelet are not friends nowadays, though their connection was clear during a televised debate on Tuesday, when they referred to each other by their first names and the familiar Spanish form of "you."
Chileans can vote from 8 a.m. (1100 GMT) to 6 p.m. (2100 GMT). Results are due shortly after voting ends. (Reporting by Alexandra Ulmer; Editing by Kieran Murray and Sandra Maler)