The Blues started on the front foot at Goodison Park, but clear-cut chances were certainly at a premium in the opening stages.
It wasn’t until almost the half-hour mark that Chelsea troubled Jordan Pickford, with Cole Palmer squaring to Nicolas Jackson, who saw his effort saved before Malo Gusto blazed his follow-up over the bar.
Minutes later, the visitors again nearly broke the deadlock, as this time, a corner delivery found its way to the back post where Jackson reacted first to head onto the woodwork before Gusto again failed to make the most of a rebound.
Everton saw little of the ball in the first half, yet a swift breakaway led by Abdoulaye Doucouré offered some promise for the hosts, who came close when Orel Mangala tested Robert Sánchez with a fierce strike.
Following their impressive 0-0 draw against title-chasing Arsenal, no side in Europe’s top five leagues had kept more clean sheets since the start of October than Everton’s six.
The Toffees were proving difficult to break down, and that served as a platform for what should have been the opener soon after the restart, yet Sánchez did exceptionally well to spread himself wide and deny an unmarked Jack Harrison from close range.
To their credit, the hosts continued to carve out opportunities as the half wore on, with Sánchez again vital in stopping Jesper Lindstrøm’s searching ball from finding a teammate.
In the end, a point apiece is likely a fair outcome given Everton’s second-half endeavour, with Chelsea’s failure to find a breakthrough meaning the Londoners won’t be spending Christmas top of the tree, instead remaining second behind Liverpool.
Merseyside rivals Everton may have only won once in eight league fixtures, but another creditable point here will do Sean Dyche no harm as his side climb to 15th in the standings.