Turnout is reportedly high, reports CBS News Correspondent Bill Gasperini. The weather is cold and clear, and voting has proceeded in an orderly fashion, with more than 12,000 foreign observers are in place all across the country.
The vote is momentous for Ukraine, a nation of 48 million people caught between an eastward-expanding European Union and NATO, and an increasingly assertive Russia, its former imperial and Soviet-era master.
Opposition candidate Yushchenko, a former Central Bank chief and prime minister, wants to bring Ukraine closer to the West, while the Kremlin-backed Yanukovych, the current prime minister, emphasizes tightening the Slavic country's ties with Russia as a means to maintaining stability.
Oresta Stepanchuk, a Kiev teacher, said she was casting her ballot for Yushchenko "because he offers us some prospects, some decent life." Another voter at the same precinct, Mykola Vladimirov, said he supported Yanukovych because "the others will sell the country to Americans."
"At least we now have a chance to live as independent people, but with him (Yushchenko) we will be no more than American slaves," he said.
Yushchenko, whose face remains badly scarred from dioxin poisoning he blamed on Ukrainian authorities, has emerged as the front-runner, building on the momentum of round-the-clock protests that echoed the spirit of the anti-Communist revolutions that swept other East European countries in 1989-90.
His backers launched the demonstrations after Yanukovych was named the winner of the fraudulent Nov. 21 presidential runoff. The Supreme Court later annulled the results and ordered Sunday's repeat vote — an unprecedented third round.
Outgoing President Leonid Kuchma said he cast his ballot hoping the results will stick. "In my opinion, the one who loses should call and congratulate the winner ... and put an end to this prolonged election campaign."
As the polls opened, smoke from cooking fires rose above one end of Kiev's stately main avenue, the Kreshchatyk, where Yushchenko supporters have camped out in a tent city for the five weeks.
"What we did during the last 30 days was a tribute to our ancestors," Yushchenko told reporters after voting in Kiev's trade union building. "I know they are looking at us from heaven and they are applauding."
Casting his ballot at a different Kiev polling station alongside his wife, Lyudmila, Yanukovych said: "I voted for the future of Ukrainian people. I am waiting for Ukraine to make the right choice."
The election crisis has opened a rift between the Russian-speaking eastern regions, which largely back Yanukovych, and the cosmopolitan Kiev and the west, where Ukrainian nationalism runs deep and support for Yushchenko is high.
"I voted for Yanukovych because I am afraid of western extremists who will steal my pension," said Galina Zhelivo, 63, who cast her vote in the prime minister's eastern stronghold of Donetsk.
The vote has also has thrown a spotlight on Ukrainians' starkly differing views of how to bring their nation into the 21st century.
Serhiy Shetchkov, 53, voted at Kiev's Music Conservatory, where election monitors vastly outnumbered the trickle of early morning voters. He said he cast his ballot for Yushchenko — "of course."
"He is an economist and that's what the country needs right now," he said after putting his pen-marked ballot into a transparent box. "I'm not as interested in all this talk about the European Union versus Russia. I'm interested in someone who can raise the standard of living, raise pensions, create more jobs."
Despite the huge presence of foreign observers, both campaigns complained of some violations. Yanukovych's campaign complained that Yushchenko campaign material was found near some voting booths. Yushchenko's headquarters, meanwhile, complained that the names of Ukrainians who had died were included on a voter list in Donetsk.
On Saturday, the Constitutional Court ruled against some amendments passed earlier this month that would have allowed only people with certain disabilities to vote at home. The court said all those unable to reach polling stations because of a disability or ill health be allowed to vote at home.
Yanukovych enjoys strong backing from elderly and disabled Ukrainians who saw their pensions raised twice during his time as prime minister, and he had pushed for the restrictions to be lifted, saying they would deprive millions of their right to vote.
But it was unclear if the ruling would help or hurt his prospects. His campaign workers had planned to ferry many homebound elderly to the polls, and logistics may prevent more from taking advantage of the last-minute ruling.
"The court's decision 15 hours ahead of the vote was a bitter pill for democracy," Yushchenko said. "I asked all members of my staff to send their own cars to help the disabled to get to the polling stations."