The president, who is seeking a fourth six-year term, urged all political parties Saturday to prepare themselves mentally and emotionally to accept the outcome of the vote, saying in his words "the world will not come to an end for anyone."
Mr. Chavez is facing his most formidable opponent in almost 14 years in power -- 40-year-old Henrique Capriles, a lawyer.
Most pollsters say the president is winning the race, but Mr. Capriles' popularity continues to rise.
The national electoral council says close to 40,000 polling stations have been set up around the country.
A nagging question in the race is the president's health. Mr. Chavez says he has fully recovered from the cancer that was first discovered more than a year ago.
The 57-year-old leader has undergone two surgeries to remove tumors from his pelvis, plus several radiation treatments in Cuba since his initial diagnosis. The exact nature of his cancer has never been revealed.
Mr. Chavez insists his treatments have not depleted his energy.
If he wins, Mr. Chavez could serve until 2019, which would mark his 20th anniversary as Venezuela's president.
Some information for this report provided by AP, AFP and Reuters.