Joe Rindl, BBC Sport
Chelsea have turned a corner in recent weeks.
Mauricio Pochettino's side are unbeaten in their past 10 home matches, and reached the Carabao Cup final on Tuesday night with a thumping 6-2 aggregate win over Championship side Middlesbrough.
Finishing though remains an issue.
Palmer looked lively for the eight-time winners and should have scored midway through the second period after intercepting a Martinez clearance, but miskicked his shot in the penalty area.
Chelsea looked frustrated in the closing stages and worryingly did not record a shot after the 63rd minute.
But manager Mauricio Pochettino put that down to Villa, who were playing their first match in 12 days, having a lot more rest than his side who beat Boro three days ago.
"I think it was a very good game," Pochettino told BBC Sport. "I think we dominated more of the beginning, then in the second half, after 70 minutes, we start to drop our energy.
""I am so happy with the performance of the whole team, I think the performance was good we just weren't clinical enough.
"For them to face a team like Aston Villa who are doing fantastic in the Premier League and are in the top four, I think it's a very good signal that we are improving."