Acting President Nicolas Maduro was chosen by Mr Chavez (pictured) as his successor
People in Venezuela are voting in a presidential election, called after the death of Hugo Chavez.
Acting President Nicolas Maduro, chosen by Mr Chavez as his successor, is running against Henrique Capriles, currently governor of Miranda state.
Mr Capriles narrowly lost to Mr Chavez in elections last October.
On the eve of polls opening, he accused Mr Maduro of breaking elections laws by continuing its campaign on state television.
Mr Maduro, aged 50, whose campaign has focused on his close relationship to Mr Chavez, was shown visiting the tomb of the late leader, a move Mr Capriles, 40, said was "violating all the electoral norms".
The BBC's Will Grant in Caracas says both candidates have to some extent broken the media silence they are supposed to have maintained since campaigning officially ended on Thursday.
Almost 19 million Venezuelans will have the right to vote on Sunday.
Voting is electronic - one machine will identify voters' fingerprints, and a second will recognise identity card numbers and register the vote anonymously.
Polls opened at 06:30 local time (11:00 GMT) and will close 10 hours later, although they will stay open until all those queuing at closing time have voted.
The former president died on 5 March, after a two-year long battle against an undisclosed type of cancer, prompting a short electoral campaign period before Sunday's elections.
The winner is due to be sworn in on 19 April and serve until January 2019, to complete the six-year term that Mr Chavez would have begun in January.
Mr Chavez's handpicked candidate Nicolas Maduro is seen as the front-runner, but recent polls suggested the gap between him and his rival, Mr Capriles, was narrowing.
"My vote will be for Maduro, but my heart will be with Chavez," Alejandro Almeida, 67, a retired factory worker, told the French news agency AFP.
But opposition supporter Alexis Chacon, 74, who runs a chemical company, said he was "terribly disappointed" with the current situation in oil-rich Venezuela.
"The Hugo Chavez nightmare has sunk this country," he told AFP.