Socialist Michelle Bachelet romped to an easy win in the first round of Chile's presidential election on Sunday but now faces a showdown with rightwinger Evelyn Matthei.

Ms Bachelet, who was president between 2006 and 2010, is widely expected to win the December 15 run-off triggered after she failed to attract an absolute majority.

If she does win she will face a tough second term.

The precise balance of Congress - also elected yesterday - remains undetermined, but while her New Majority coalition achieved the simple majority needed for tax changes it didn't win enough seats to change the electoral system or constitution.

Pinochet-era rules require voting majorities in Congress of 57 per cent for educational reform, 60 per cent for electoral reform and nearly 67 per cent for constitutional changes.

The congressional election results mean that the New Majority will need other parties to support reforms promised by Ms Bachelet.

Chile has for many years seen angry street protests to demand far-reaching changes to the country's power structure and the reversal of policies dating from the era of the Pinochet dictatorship that foster vast inequality.

She left office with an 84 per cent approval rating after her 2006-10 presidency despite achieving major changes.

This time she has taken up the cause of protesters, vowing to revamp the constitution, raise corporate taxes to 25 per cent from 20 per cent to fund an education overhaul and reduce the wealth gap.