The candidate will be chosen by a committee of mostly pro-Beijing electors, rather than a public vote, which pro-democracy campaigners have been fighting for.
Carrie Lam, deputy to the current leader, is China's choice for the role and is expected to win.
Ahead of the vote, around 1,000 people took to the streets to demand a greater say in who will lead Hong Kong.
Mrs Lam's main rival, former finance chief John Tsang, is the public's favourite, according to opinion polls.
The third candidate is retired judge Woo Kwok-hing.
Calls for fully free elections in the semi-autonomous region have failed, despite intense demonstrations, known as the "umbrella protests", in 2014.
Hong Kong's 1,200-seat Election Committee will pick one of the three candidates to succeed current leader CY Leung, who steps down in July.
Mr Leung has proved unpopular will large swathes of Hong Kong residents who consider him too tightly aligned to Beijing.
At the end of the 2016, he made the unexpected announcement that he would not run again, citing family reasons.
His successor will need 601 votes to win. If no candidate reaches this total, the top two candidates go to a second round.
Mrs Lam is nicknamed the nanny because of her background running numerous government projects, while Mr Tsang is referred to as Mr Pringles because he resembles the moustachioed character on US crisp packets.
If Mrs Lam wins, she would become Hong Kong's first female chief executive.
During the 2014 protests, the long-time civil servant took the unpopular stance of defending Beijing's concessions for political reform - allowing Hong Kong people to choose their leader but only from pre-approved candidates.
Hong Kong is governed under the principle of "one country, two systems", under which China has agreed to give the region semi-autonomous status since its 1997 handover from Britain.
Hong Kong's Election Committee includes 70 members of the Legislative Council - half of whom are directly elected.
However, most of the committee is elected by business, professional or special interest groups.
Critics say entities that lean towards Beijing are given disproportionately large representation.
Last year, pro-democracy activists secured 325 seats on the committee - the highest number ever. However, this does not give them enough seats to determine who becomes the next chief executive.
(Photo: China-backed Carrie Lam (left) and her rival John Tsang)