Anelka strike enough for Chelsea
The France striker, who netted the only goal in Chelsea's victory over Porto at Stamford Bridge in their tournament opener, produced a fine finish from Juliano Belletti's cross after 18 minutes.
Chelsea dominated possession for long periods but the Cypriot side threatened after the break and Petr Cech had to save with his legs after Savvas Poursaitides's shot took a deflection.
"I am not satisfied, Chelsea have to play better," said coach Carlo Ancelotti. "We made a lot of mistakes, Nicosia played very well and deserved to draw the game. But this is football.
Chelsea failed to build on their good start and APOEL, roared on by over 20,000 fans, began to stretch the Premier League side's defence in the second-half but could not find a way to beat Cech.
"I think we wasted 45 minutes," said APOEL coach Ivan Jovanovic. "It was an easy first half for Chelsea, they scored and controlled the game.
"We are satisfied with the performance of the second half, we managed to control the pace of the game. That's probably why we are a bit disappointed. We made an exceptional effort in the second half," the Serbian coach said.
Chelsea top the group with six points while APOEL have one.