more than six decades since independence through a peaceful struggle and then a bloody civil war, but failed.
However, Saturday's elections are expected to give them a limited say in their own affairs - a taste of democracy after decades under rebel or military control.
The elections are seen by the United Nations and the world community, as a crucial test of reconciliation between the Tamils and majority ethnic Sinhalese, who control the government and the military.
"Our political problems must be resolved, another generation must not be destroyed," said Rasathurai Balasubramanium, a 56-year-old mason after voting in his village Thavadi.
"We believe that there is a ... (slice) of democracy and law and order is still available in this country," said Gunaratman Manoharan, a 52-year-old businessman who traveled from the capital, Colombo, to vote.
The country's ethnic divisions widened with the quarter-century civil war that ended in 2009, when government troops crushed the Tamil Tiger rebels who fought to create an independent state.
At least 80,000 people were killed and northern cities, including many in Jaffna peninsula, were reduced to rubble.
The Tamil National Alliance, considered a political proxy for the Tamil rebels during the conflict, is the favorite to win the election and has fielded a former Supreme Court Justice, C.V. Wigneswaran, as its chief candidate.
More than 700,000 voters are registered to elect 36 members to the provincial council, which will not have much power. A governor appointed by the central government retains almost all of the control, and Wigneswaran says if elected his party would lobby for wider self-rule based on federalism.
But the central government is against devolving such wide powers and says even existing powers in provincial hands, such as those over land and policing, are a threat to the country. It hopes to win over Tamils by rebuilding roads, schools, hospitals and other infrastructure destroyed in the war.
But residents say the army is taking over large swathes of private land to build camps and even businesses such as hotels, and bringing in Sinhalese people to change the province's ethnic breakdown.
Angajan Ramanathan, a 30-year-old businessman and the leading candidate for President Mahinda Rajapaksa's Sri Lanka Freedom Party, says working close to the government will bring more benefits to the war-hit community.
Campaigning has been marked by sporadic attacks and threats, mainly against Tamil Alliance supporters.
In the latest incident, an election monitor said soldiers armed with clubs attacked supporters of Tamil Alliance candidate Ananthi Sasitharan at the candidate's home late Thursday, wounding eight people.
Sasitharan, the wife of a former Tamil Tiger rebel leader, escaped unharmed, said Keerthi Tennakoon of the Campaign for Free and Fair Elections.
Tamils have been demanding regional autonomy to the country's north and east, where they are the majority, since Sri Lanka became independent from Britain in 1948.
The campaign took the form of nonviolent protests for many years, but in 1983 civil war broke out between government forces and armed Tamil groups calling for full independence.
The provincial council was created in 1987 as an alternative to separation. But the Tigers - the strongest of the rebel groups, and eventually the de facto government across much of the north and east - rejected it as inadequate. The fighting that followed prevented the council from functioning.
The military defeat of the Tigers meant Tamils were back to where they had started 60 years earlier.
The U.N. welcomed the election in a statement, calling it an "important opportunity to foster political reconciliation."
The U.N. has called on Sri Lanka repeatedly to more thoroughly investigate war crimes committed by both sides. A U.N. report has indicated Sri Lankan troops may have killed as many as 40,000 Tamil civilians in the final months of the conflict.
The Tigers are also accused of killing civilians, holding them as human shields and recruiting child soldiers.
The U.N. estimates that 80,000 to 100,000 people died in the conflict, but the number is feared to be much higher. Few outsiders had any access to combat zones in the bloody final phase of the war.
The Tamil Alliance has said if it wins control of the provincial government, it also will push for an international war crimes investigation.