* 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 early results)
By Alexandra Ulmer
SANTIAGO, Dec 15 (Reuters) - Former President Michelle Bachelet took a lead in Chile's presidential election on Sunday, with early results indicating that the center-leftist would easily beat her conservative rival.
Bachelet had about 61 percent support with her ruling party rival Evelyn Matthei trailing on around 39 percent, with 2 percent of votes counted, according to electoral service Servel.
In Chile's first presidential showdown between two women, the majority of voters were expected to back Bachelet, who led the country from 2006 to 2010, wooed by her easy charm and plans to tackle deep income inequality.
Sharp-tongued 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.
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." (Additional reporting by Rosalba O'Brien; Editing by Kieran Murray and Sandra Maler)