They are the first legislative polls to take place in the war-torn region since 1997. Chechnya is the only Russian republic that currently has no parliament.
For the Kremlin, the polls are intended as the final stage in the process of "normalization" that reportedly started with the adoption of a new constitution in March 2003.
According to Chechnya's new constitution, the parliament is made up of two chambers.
The upper house, or Republic's Council, will have 18 members elected from single-mandate constituencies. The lower house, or People's Assembly, will be made up of 40 parliamentarians -- half elected from single-mandate constituencies, half from party lists.
Some 350 individual candidates and seven parties are taking part in the polls.
Candidates include a number of Russian Army officers and many officials with the pro-Moscow regional administration.
Kadyrov Line
Regional analysts believe candidates loyal to Deputy Prime Minister Ramzan Kadyrov -- the son of late pro-Russian President Akhmad Kadyrov -- will win a majority of seats in both houses. Ramzan Kadyrov was named acting prime minister after Prime Minister Sergei Abramov earlier this month was injured in a car crash in Moscow.
Talking to Russian reporters after casting his ballot, Chechen President Alu Alkhanov said he hoped the new parliament would help normalize the situation in the republic.
"Today, the population expects the parliament to work actively with the government toward improving their living standards. The parliament must ensure that the economy becomes more efficient and that laws are voted that will help market economy and investments develop with the greatest possible speed and efficiency," Alkhanov said.
Russian media has reported that turnout in today's polls is particularly high, something that some Russian commentators have said testifies to Chechnya's thirst for stability.
Ramzan Kadyrov told Russia's ITAR-TASS news agency that more than one-fourth of Chechnya's 600,000 registered voters had already cast their ballots by 1300 local time. According to the Chechen Constitution, at least 25 percent of voters should turn out for the elections to be technically valid.
Doubts About Political Process
Russian human rights groups, however, have described the vote as a simulacrum of a political process.
In a 60-page report issued this week, a coalition of Russian and western rights groups denounced the climate of fear that reigns in Chechnya.
The report also criticizes the Kremlin's policy of progressively transferring its responsibilities to the pro-Moscow administration.
That policy, rights groups say, has not brought peace to Chechnya. On the contrary, they say it has led to the further spread of fear and insecurity among the population.
The Chechen separatist leadership in turn has denounced the polls as a political "farce" that will lead to the further expansion of the theater of war.
Akhmad Zakayev, the exiled deputy prime minister of the separatist government, said in London on 26 November that the election will "push further away the day when there will be a real political solution in Chechnya."