The atmosphere in the capital of Grozny was tense on Sunday after a man blew himself up when police approached him outside a polling station. Nobody else was injured in the blast.
"The attention of the guards was drawn to a young man with a plastic bag who was going into a polling station. When they asked him to stop and show his papers, he ran off and an explosion occurred," election official Salamu Vakhidov said.
Up to 14,000 Chechen police are patrolling the streets of the country alongside Russian forces.
"Everything has been done to conduct normal, free, democratic elections," chief electoral officer Abd Al-Karim Arsakhanov told Rossiya state television.
Kremlin-backed candidate Alu Alkhanov is virtually certain to win the poll, but many doubt his ability to rein in separatists.
Separatists have fought for a decade to win independence for their largely Muslim Caucasus homeland and push out Russian forces.
Many Russians see control over Chechnya as crucial to the unity of a vast federation linking dozens of ethnic groups.
That belief boosted Russian President Vladimir Putin's popularity in 1999, but early military successes soon turned into a guerrilla war of attrition with the separatists.
Attacks by separatists, however, appear to have done little so far to dent his popularity in the rest of Russia.
Separatists assassinated President Akhmad Kadyrov in a May bomb attack that exposed the precarious nature of Russsian rule. They vow to kill Alkhanov as another "Moscow stooge".
Observers say Moscow's support for the career policeman may reduce his popularity among Chechens.
Russia's President Putin (L) backs
chief candidate Alu Alkhanov
Officials have so far refused to blame Tuesday's double air crash on separatists. Explosives have been found in both planes' wrekages.
Some fear the crashes could be part of a new wave of attacks to coincide with the elections. The crashes followed a weekend attack on Grozny that killed as many as 120 people.
Putin has made his support for Alkhanov clear, regularly appearing in public with him. State television features Alkhanov daily, ignoring his six unknown rivals.
"I do not rule out that the results will be rigged," candidate Movsur Khamidov, an officer in the FSB security service, said. "The town is empty because of the violence on 21 August. I think violence will continue."