The Spain international scored twice in the west London side’s 6-3 victory over Everton at Goodison Park on Saturday.
Costa has scored four goals in three Premier League games following his £32m switch to Stamford Bridge from Atletico Madrid this summer.
And Drogba, who sealed a return to the 2012 Champions League winners in the current transfer window, talked up the 25-year-old’s qualities.
“Diego Costa has started very well,” Drogba said. “He looks special. He’s scoring goals and helping the team. He’s settled right in – and he’s started much better than I did!”
Costa was part of the Atletico Madrid side that won La Liga in May before losing to bitter rivals Real Madrid in the Champions League final in Lisbon.
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