Indeed, the Spaniard was again a thorn in the north London club's side on Sunday afternoon, bursting forward only to be brought down by Per Mertesacker.
The German was subsequently sent off and Costa scored Chelsea's winner against Arsenal five minutes later.
His relationship with fans at the Emirates has always been a tense one and supporters duly made their feelings clear towards the 27-year-old throughout proceedings on Sunday.
However, Shearer believes Costa will only feed off that kind of energy and has questioned why Arsenal fans are doing Guus Hiddink's motivating for him.
Costa was always going to pose a problem for Arsenal and Hiddink looked happy enough to shut up shop and hold out for all three points after half-time.
Arsenal came at the Blues in the second half but, with 10 men, they were always going to find it difficult to break Chelsea down.
Job done for Costa - and maybe Shearer has a point here?
Looks like Chelsea have done the best business this window with their 12 new signings....— Alan Shearer (@alanshearer) January 24, 2016