Socialist champion Michelle Bachelet will head in to the second round of Chile's presidential race as clear favorite but with too thin a parliamentary majority to guarantee planned constitutional reforms. Bachelet was Chile's first female president between 2006 and 2010 and, having comfortably won Sunday's first round of voting, is now on course to return to office after the December 15 run-off. But her "New Majority" alliance of socialists, Christian Democrats and communists was projected Monday to take only 68 of 120 seats in the lower chamber of parliament and 21 of 38 in the Senate. With all but a tiny fraction of first round votes counted, 62-year-old Bachelet had won 46.67 percent of the vote against only 25 percent for her conservative rival, 60-year-old Evelyn Matthei.