At a ceremony in Warsaw the president of European football's governing body, Michel Platini, presented Pawel Michalczak, a 34-year-old forester who lives near the Polish capital, with his prize of a ticket for Poland's three first-round matches.
"Of course I can't guarantee you'll get to see them in the second round too," Frenchman Platini joked, speaking in Italian as his former Juventus team-mate and ex-Poland icon Zbigniew Boniek translated.
Michalczak won his tickets in a competition organised by UEFA for Polish fans.
"I couldn't believe it when I got the call. I thought someone was trying to sell me something," Michalczak said.
"Then I thought it was my friends playing a bad joke. Now I'm just really happy," he added, noting that he had failed to see the 2006 World Cup in Germany and Euro 2008 in Switzerland and Austria.
Platini drew the name of a second Poland fan -- Ewa Lewczuk -- at the ceremony itself and telephoned her live from the stage.
"This is fantastic. It's not a joke?" said Lewczuk as she learned she would get four tickets for Poland's June 8, 2012 game in Warsaw, which kicks off the entire tournament.
"My husband and son are massive fans. And I'm overwhelmed," she added.
At a similar ceremony in Kiev, capital of Poland's fellow host nation Ukraine, UEFA executive member Frantisek Laurinec handed over four tickets for the country's June 11 opener to primary school teacher Vita Lavrenko, who was accompanied by her young son.
Other fans hoping to see the 16-nation championships will have to get lucky another way.
More than 550,000 tickets are available for the general public but demand traditionally far outstrips supply -- 10.4 million people applied for 300,000 tickets at Euro 2008.
From Tuesday until the end of this month, would-be buyers must sign up at the ticket portal on UEFA's website, uefa.com, which it repeatedly has underlined is the only authorised channel.
In April, it will decide by lottery who gets to purchase a ticket.
On Tuesday, 591,000 people had already applied, 70 percent of them from Poland and fellow host nation Ukraine, and the rest from 159 other countries, UEFA officials said.
The ticket portal was swamped, displaying a screen reminding fans that it is not first come, first served.
UEFA's ticket sales manger Rainer Berak hammered home that message in Warsaw.
"There's no danger of missing out if you don't rush to the portal today. You can apply in the next few days or weeks and you'll have the same chance. You've got the whole of March," Berak told reporters.