It was the same outcome as the men's fixture between the two clubs last Sunday and the Blues remain two points clear of the Gunners going into their FA Women's Cup semi-final against Manchester City on Monday.
Chelsea 0-0 Arsenal
The FA WSL1
7.30pm, Thursday 30 May 2015
Wheatsheaf Park, Staines Town
By Pippa Field
The first half proved to be very cagey with Ji So Yun dragging a shot wide for Chelsea and Arsenal's Natalia Pablos Sanchon hitting a long-range effort over.
Matija Banusic had a shot from distance comfortably saved by Emma Byrne as the players went off for half-time without a breakthrough being made.
Early in the second half, Jemma Rose had to make a brave block from point-blank range to deny Gemma Davison after she controlled Hannah Blundell's cross.
Ji wasted the best chance of the match on 63 minutes as she blazed over under no pressure after being set up by Jackie Groenen, who had caught Jade Bailey in possession.
Chelsea goalkeeper Hedvig Lindahl was then let off the hook as Chioma Ubogagu shot tamely at her after her poor clearance had only gone as far as Rachel Yankey on the edge of the area.
Blues captain, and former Arsenal star, Katie Chapman admitted after the game that it was probably a fair result.
Highlights of Thursday's FAWSl clash at Staines Town
"I think the game was pretty even and it was the right result, to be quite honest," said the England international.
"Both teams didn't create many good chances and it was quite a scrappy game.
"We weren't happy with that performance because we felt it could have been better but hey, we didn't lose.
"I thought we were resilient in our performance, we stuck together as a team and obviously we didn't concede so we still haven't lost a game and that's massive this season.
"I think Arsenal are always a force - I've been there and I've played for that club and they always bring through good players so we knew it was going to be a tough game."
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Chelsea (4-3-3): Hedvig Lindahl, Ana Borges (Claire Rafferty 75), Niamh Fahey, Gilly Flaherty, Hannah Blundell, Jackie Groenan, Katie Chapman, Laura Coombs (Millie Bright 45), Marija Banusic (Eniola Aluko 53), Gemma Davison, Ji So-Yun
Substitutes not used: Marie Hourihan, Jodie Brett, Anne Meiwald, Drew Spence
Arsenal (4-3-3): Emma Byrne, Alex Scott, Casey Stoney, Jemma Rose, Emma Mitchell, Jade Bailey, Jordan Nobbs (Lianne Sanderson 10), Vicky Losada, Chioma Ubogagu, Danielle Carter, Natalia Pablos Sanchon (Rachel Yankey 75)
Subs not used: Hollie Augustus, Carla Humphrey, Chloe Kelly, Caroline Weir, Taome Oliver
Referee: Nigel Lugg