The powerful striker has netted in both the Blues' game so far as they recorded wins over newly-promoted Burnley and Leicester City.
The Spain international moved from Atletico Madrid earlier this summer, with a little scepticism about his ability to transfer his talents from La Liga to the Premier League.
The doubters saw no reason to change their stance when Costa floundered with La Roja at the World Cup as Vicente del Bosque's side weakly surrendered their 2010 crown in Brazil.
Spain were sent home at the group stages as Costa fluffed his chance to lead his adopted nation in the country of his birth.
In truth, Costa had probably not been fully match fit since he limped out of the first leg of the Champions League semi-final against Barcelona back in April. He lasted just nine minutes of their defeat against fierce local rivals Real Madrid in May's final, and laboured in Brazil.
After enjoying a good, injury-free pre-season, however, the swashbuckling striker is starting to show exactly why Jose Mourinho was so keen to sign him.
Costa is purpose-built for the terrain of the Premier League. The burly 25-year-old can bully defences on his own, and he will be Chelsea's main man up top this season, with Didier Drogba and the much-maligned Fernando Torres acting as back up to the ex-Los Rojiblancos star.
A key member of the Atleti side that broke the duopoly of Real Madrid and Barcelona last season; his 27 goals went a long way to seeing Diego Simeone's side achieve what many thought was impossible.
Despite being a Brazilian-born Spanish striker, his rugged approach to the art of centre-forward play is exactly what Chelsea were crying out for last season, and with the likes of Eden Hazard, Willian, Cesc Fabregas and Andre Schurrle feeding off him, the Blues will be expected to challenge for honours this season.