A party led by a former Kosovo Albanian guerrilla leader has won the breakaway province's parliamentary election, according to unofficial results.
Hashim Thaci has promised to declare formal independence from Serbia after 10 December - the UN deadline for Albanians and Serbs to reach a deal.
It seems likely his party will have to form a coalition with bitter rivals.
Serbs, who want Kosovo to remain part of Serbia, boycotted the polls, which saw a record low turnout.
If Mr Thaci's party did in fact win the largest number of seats in the 120-seat parliament, a period of negotiations is likely to take place before a coalition government is formed, the BBC's Nick Hawton reports from the Kosovo capital, Pristina.
But every ethnic Albanian party, our correspondent adds, has the same priority: trying to make Kosovo an independent state in its own right and break away from Serbia.
EU Enlargement Commissioner Olli Rehn called for the "rapid formation" of a new government and urged Kosovo's new leaders to "work constructively for a sustainable status settlement".
Kosovo is formally part of Serbia but has been run by the United Nations since 1999 when Nato ejected Serbian forces from the province.
"We will declare independence immediately after 10 December," Mr Thaci told cheering supporters as results were coming in.
"With our victory today begins the new century... Today Kosovo citizens sent a message to the world, that we are a democratic society, that we are ready to take our country towards the European Union."
Mr Thaci's Democratic Party had won 34% of the vote with more than 90% of ballots counted, independent observers said.
That puts the former leader of the Kosovo Liberation Army in pole position to be prime minister.
The rival Democratic League of Kosovo, which has dominated Kosovo politics since independence, trailed in second place with 22% of the vote, election monitors said.
Official final results may take several days to come through.
According to election officials, the turnout was around 45%, the lowest since 1999.
Council of Europe representatives described the turnout as "alarmingly low".
Correspondents say the low figure was down to poor weather and disenchantment with economic prospects, not second thoughts about independence.
One hundred of the 120 seats in the provincial assembly were up for direct election, with the rest reserved for Serbs and other minorities.
The Serbian government had called on ethnic Serbs not to vote so as to avoid legitimising the new government.
A Kosovo Serb spokesman, Rade Negojevic, said just three out of 46,000 Serbs in northern Kosovo had cast ballots.
"Two people voted in Leposavic district, one in Zvecan and not a single person in Kosovska Mitrovica," he said.