James McAtee's strike on the hour-mark proved decisive, before some great saves from Cieran Slicker secured Brian Barry-Murphy's side the three points and sent us above West Ham to the top of the table.
The first half featured very few chances for either side, but City were mostly in control of proceedings at the Cherry Red Record Stadium.
Kayky worked some space on the edge of the box in the sixth minute and fired in a fierce cross only for it to be cut out by Teddy Sharman-Lowe, and a deflection denied Josh Wilson-Esbrand, whose right footed shot was blocked before it could trouble the Chelsea keeper.
The hosts looked dangerous on the counter attack and could've taken the lead when Jude Soonsup-Bell took down a long ball, beating our offside trap only to shoot high and wide as Slicker was kept relatively quiet in the City goal.
McAtee, Kayky and Oscar Bobb continued to try and craft chances for City up the other end of the pitch, but were unable to create many clear-cut opportunities, with Chelsea's defence standing strong to ensure we went into the half-time break goalless.
Luck was on our side soon after the restart when Soonsup-Bell's header cannoned off the City post, before half-time substitute Sammy Robinson produced a well-timed challenge to snuff out a counter-attack from the hosts.
But City finally found the breakthrough on the hour mark when, from a corner, the ball found its way to McAtee inside the area.
Taking a touch and working some space, the youngster slid the ball under the despairing dive of Sharman-Lowe from a tight angle to hand us a well-deserved lead.
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But Chelsea reminded us soon after that the game was far from over, with Slicker was called into action to deny Charlie Webster from close range in the 70th minute, before producing a fingertip save to deny Jayden Wareham from inside the area.
The City keeper was forced into making another vital block in the last ten minutes as Wareham tried to hook the ball home from a corner.
City nearly added a second late on as Egan-Riley's ball into the box bounced off the crossbar with the Chelsea keeper back-pedalling, but Brian Barry-Murphy's men had to settle for a single goal victory to secure a vital three points.
HOW WE LINED UP
Cieran Slicker started between the sticks for City and he was guarded by a four-man defence consisting of CJ Egan-Riley, Finley Burns, Luke Mbete and Wilson-Esbrand.
Romeo Lavia provided defensive cover in midfield alongside Kian Breckin, who retained his spot following his EDS debut against Manchester United.
James McAtee played in the No. 10 role, flanked by Kayky and Carlos Borges whilst Oscar Bobb was named up front.
WHAT IT MEANS
Our win over Chelsea took us to the top of the Premier League 2 table, climbing one point above West Ham following their earlier defeat to Leicester, although the Hammers still have a game in hand on us.
Next up for the EDS in the Premier League 2 is an away trip to Derby County.
Kick off is at 19:00 (UK) on Monday 7 February with the match available to watch live on CITY+.
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