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The Londoners, who have won their first four league games and scored 17 goals in the process, cruised to a 3-0 halftime lead with two goals by Nicolas Anelka and one for Michael Essien.
Daniel Sturridge added the fourth three minutes after the restart with Tomas Oravec nabbing a consolation for the Slovakian hosts.
It was just the start Chelsea manager Carlo Ancelotti would have asked for in a fixture that could easily have been an awkward trip.
However, even without suspended striker Didier Drogba and injured midfielder Frank Lampard, Chelsea had more than enough firepower to continue their free-scoring start to the season.
They went ahead after 13 minutes when Yossi Benayoun, making an impressive first start since his summer arrival from Liverpool, sent Anelka clear and when the Frenchman squared for Essien the midfielder sidefooted in his third in two games.
After 24 minutes Florent Malouda chipped a nice pass into the path of Anelka and the striker slotted it underneath the keeper with the minimum of fuss.
It was soon three as John Terry headed a corner against the bar and Anelka seized on the rebound to score from point-blank range.
Three minutes after the restart Benayoun sent Sturridge through and the forward duly tucked in his first European goal.
Zilina had looked completely outclassed but they showed admirable grit to fight back.
Their goal was somewhat fortunate, though, as the ball pinged off Chelsea defender Alex and Oravec almost burst a blood vessel to get a toe to it just before it crossed the line. Chelsea will have much tougher games along the road but did a thoroughly professional job as they seek that elusive Champions League title having reached the semi-finals four times in the last six years.
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