The Brazil-born Spain international took his tally to four in three matches after his £32million move from Atletico Madrid with two in the frenetic 6-3 win at Everton.
Costa's goals helped his former side to the Spanish title last season after he got off to a rapid start with 10 in eight successive wins from the off.
Twelve months on Costa shows no signs of slowing down despite the hamstring problems which disrupted the end of his campaign.
"We have started really well and it is always good to have a great start," he said
"Last year we did the same and now this year too
"It is nice to score goals but for me the most important thing is the team wins but I am happy I scored and helped the team win.
"Our team is a great team, it is really important to achieve great things and I am really happy to be here."
Costa scored in the first minute - after just 35 seconds - and the last, in between which were sandwiched efforts from Branislav Ivanovic, Nemanja Matic and Ramires in addition to a Seamus Coleman own goal.
Kevin Mirallas, Steven Naismith and, against the club he left in the summer, Samuel Eto'o made it 2-1, 3-2 and 4-3 respectively but Chelsea always just kept one step ahead.
"It was nice to score my first goal (for the club) because on this ground it is always difficult, although the most important thing is we got three points," said midfielder Matic.
"This season we play better, we have more goals in us, we are more confident in attack - we scored six goals which is not easy.
"It was very good for people who bought tickets for the game as they saw nine goals, which is good for football and the Premier League.
"If every game was like this I'd be happy but the coach will show us where we made mistakes."
The coach in question, Jose Mourinho, has many examples to show them on Monday morning after expressing his dissatisfaction with how they defended.
But he also gave them some credit for the way they attacked clinically.
"We have scored nine goals in two Premier League games against teams in the top five last season," he said.
"The quality of our football was fantastic: every time we had the ball we were aggressive.
"I prefer to win 6-0 playing fantastic football, defensively and offensively, but I want the team to play the way we did, I want them to be positive but not make defensive mistakes."
Everton manager Roberto Martinez will have a whole DVD of errors to show his shell-shocked squad with their defensive confidence in tatters after conceding 10 goals in three matches.
The Spaniard admits fear has crept into their game and he will have to work hard to stop it.
"We started the game very uncharacteristically for us," he said.
"We didn't have that defensive intensity and focus you have to have, especially with a team like Chelsea, and then we were chasing the game.
"We were very good going forward, I don't think there will be many teams who will score three goals against Chelsea this season, but we were too soft with our defending.
"Every time the ball was around our 18-yard box we had a real fear of it ending up in our net.
"We now have conceded in three games and that is not like us at all
We kept 15 clean sheets last campaign.
"We need to work and focus
It is not the technicality of conceding goals, it is the feeling.
"That is something we need to change
Our attacking play was phenomenal and we need to bring that confidence into our defensive play."
Source : PA
Source: PA