This is the second election in the province since the 1998-99 war between Serbian forces and ethnic Albanian separatists.
The vote on Saturday for the 120-seat assembly is seen as a test of the international community's efforts to build a multi-ethnic democracy in the southern Serbian province, administered by the United Nations since Nato forced Serbian troops to withdraw in June 1999.
But it has been marred by calls for ethnic Serbs to boycott the vote over security fears after 19 people died when mobs from the ethnic Albanian majority rioted through Serb villages in March, the worst violence since the war.
More than 1000 extra Nato peacekeepers have been deployed to Kosovo to secure the election.
The Kosovo force, KFOR, is already the North-Atlantic alliance's biggest mission with about 19,000 troops in the field.
"KFOR will play its full part in maintaining a peaceful environment, and NATO has deployed additional forces into Kosovo and the region to demonstrate our capability and our resolve," Nato chief Jaap de Hoop Scheffer said on Friday.
Kosovo police spokesman Refki Morina said police were also out in force, with all 6000 local officers on duty "to ensure security and safety".
Kosovo's chief UN administrator, Soren Jessen-Petersen, said the election marked a "turning point" and would set the stage for a UN review of democracy standards early next year and possible talks on final status.
More than 1000 extra Nato
troops have poured into Kosovo
Ethnic Albanians demand complete independence from Serbia, but ethnic Serbs and the government in Belgrade insist that the territory is an inalienable part of the former Yugoslav republic.
"Kosovo's Serbs need legitimately elected leaders who can engage with the challenges ahead," Jessen-Petersen wrote on Saturday in the International Herald Tribune.
He said security was a top priority and urged Serbs to vote, while calling on Serbian Prime Minister Vojislav Kostunica to drop his support of the boycott.
"Attempting to block Kosovo's Serbs from realising their democratic rights not only hurts them but also hinders the progress of the rest of the region," he said.
"Since ethnic Albanians rioted against minority Serbs in March, the damage has begun to be repaired and Kosovo has moved forward."
About 1.3 million Kosovo residents and nearly 100,000 displaced people are eligible to vote for deputies in the provincial parliament, which has responsibility for day-to-day matters under the more powerful UN administration.
More than 1600 polling stations opened across the province at 7am (0500 GMT) and were to close at 8pm, with about 12,000 local and international observers on hand to look for irregularities.
Analysts believe a boycott will deprive the Serbs of legitimate leaders to participate in any future talks on the province's status, and the future of the UN protectorate.
On the other hand, Kosovo Albanians expect the new assembly to provide a provisional Albanian-dominated government that will prepare for final status talks with the UN, tentatively set for mid-2005.
More than 33 political groups and 30 independent candidates are taking part in the election. The latest surveys show that no party will win enough votes to control the parliament and form a government by itself.
The first unofficial results are expected this weekend.