Liverpool topped the Premier League standings at Christmas, after Arsenal and Chelsea played out a bleak 0-0 draw in the London derby at the Emirates.
Festive cheer was in short supply during a turgid 90 minutes in which Chelsea came closest to victory when Frank Lampard's first-half volley cannoned off the underside of the crossbar.
The result leaves Liverpool on top of the table ahead of the Gunners on goal difference.
Chelsea moved back into fourth spot, above Everton on goal difference, two points behind the top two in the table.
But Liverpool's chances of staying on top at New Year appear slim, with an away game at third-placed Manchester City coming up next - City have played eight, won eight at home.