Stamford Bridge side make it four wins from four Premier League fixtures.
Chelsea hosted visitors from the Liberty Stadium with both sides claiming 100% records from their first three Premier League fixtures.
Swansea City surprisingly took the lead when John Terry, chasing back to close down a Swansea City attack, bundled the ball past Thibaut Courtois into his own net.
It looked as how Garry Monk’s side would go into the break in front but Diego Costa showed great strength to hold off a firm challenge to head past Lukasz Fabianski, his fifth goal in four Premier League fixtures.
His sixth Blues goal followed eight minutes into the second half when Cesc Fabregas played a fine one-two before laying on for Costa who fired home to give Chelsea the lead.
Mid-way through the second period and Costa had his first Chelsea hat-trick after Ramires played in inadvertent through-ball which the Spanish international slammed home.
Loic Remy made things safe for Chelsea, netting nine minutes into his debut, finding the bottom right hand corner of the net after great work from Eden Hazard and Oscar.
Jonjo Shelvey slid a consolation goal past Courtois to make the final score a little more respectable.
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