Abramovich's millions have transformed Chelsea from a promising Premier League team into trophy-laden aristocrats but until they lift Europe's ultimate club prize he will be forever frustrated.
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Wednesday's captain John Terry was the only survivor from the team who triumphed 2-0 in a Champions League qualifying match in August 2003 and the gulf in class and resources on show that night has become a chasm.
The Londoners, who have won their first four league games and scored 17 goals in the process, looked completely untroubled as they cruised to a 3-0 half-time lead with two goals by Nicolas Anelka and one for Michael Essien.
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Daniel Sturridge added the fourth three minutes after the restart with Tomas Oravec nabbing a consolation when Chelsea's attention was already wandering to their weekend appointment with Blackpool.
However, for Abramovich, and last season's league and FA Cup double-winning coach Carlo Ancelotti, the focus will remain like a laser on the Champions League final at Wembley in May.
This is Abramovich's eighth assault on the competition and having reached the semi-final four times in the last six, losing in the final in 2008, no other silverware will do.
Chelsea look well equipped to go all the way and Ancelotti used Wednesday's match to give some squad members a taste of the first team.
With striker Didier Drogba suspended, midfielder Frank Lampard and defender Ashley Cole rested, Chelsea still had more than enough firepower to continue their free-scoring start to the season.
Essien sidefooted the opener after 13 minutes, Florent Malouda chipped a nice pass into the path of Anelka for the second after 24 and four minutes later he tapped in the rebound after Terry headed a corner against the bar.
Three minutes after the restart the impressive Yossi Benayoun sent Sturridge through for his first European goal.
Zilina had looked completely outclassed but gave the 11,000 crowd something for their money - ticket prices having been hiked by 700 percent - when Oravec almost burst a blood vessel to get a toe to what was looking like an Alex own goal.
Spartak Moscow and Olympique Marseille will prove Group F tests but Ancelotti, who threw on youngsters Patrick Van Aanholt Josh McEachran and Gael Kakuta during the second half, recognised a professional job well done.
"We started very well in the first half, we played fantastic football, the second half was different," he told reporters.
"I know sometimes there are difficult times, the opponent can come back in the game, but if I have to judge the performance I am very happy because it's not easy to win 4-1 away in the Champions League.
"The key was Anelka, he played a fantastic game. He created space, he had opportunities. Sometimes we use him more wide, sometimes he plays in the middle but he shows the same skills."
Zilina coach Pavel Hapal accepted that the gulf in class was too wide. "Chelsea showed their strength and we did not match this. There were good combinations, we had chances, but the disparity was there," he said.
"It was about pla
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