Five candidates are up for the post, with dozens hoping to be elected at the district and mayoral level.
The elections are being seen as a key test of whether the province, still recovering from the tsunami in 2004, can hold a second peaceful poll.
The lead-up to the elections has been marked by bouts of violence.
Aceh, in northern Sumatra, is the only province in Indonesia that is allowed to implement Sharia law.
Separatist rebels battled Indonesian government troops for almost three decades there before the peace agreement was reached in the wake of the devastating tsunami that left some 170,000 dead in the province.
For many Acehnese this election is a vote for stability. It has been seven years of an often fragile peace for the province.
Many of the voters that slowly but steadily trickled into the voting booths still remember the days when it was not safe to leave their homes at night because of the long insurgency separatist groups waged against Indonesia.
People here are still trying to recover from two tragedies – the decades-long war and then the tsunami in 2004. Aceh is a different place now, they say, and no-one wants a return to the problems of the past.