Despite a sixth-placed finish under Mauricio Pochettino last season, the Blues hierarchy made the decision to go their separate ways with the Argentine and replace him with Maresca.
Although Chelsea opened their campaign with a 2-0 home defeat to champions Manchester City, they have since responded by accumulating 13 points from five games.
Chelsea are also the top goalscorers in the Premier League with 15 strikes to their name, their recent run leaving them fourth in the standings.
Maresca and his team are now attempting to head into the October international break with a fourth successive top-flight win when Nottingham Forest are the visitors to Stamford Bridge on Sunday afternoon.
What has Maresca had to say?
Speaking ahead of that game, and after Chelsea had defeated Gent in the Europa Conference League, Maresca was quizzed on the progress of his team.
Rather than talk up their chances in the title race, Maresca played down the possibility of being able to last the pace with the likes of Man City and Arsenal.
The Italian said, as quoted by football.london: "I really don't think we can compete with City and Arsenal. I really think that, because we are not ready.
"The reason why is that City are working with the same manager for nine years, Arsenal for five years. It's something that if you want to compete for important things, you need that time.
"After Arsenal v Paris St Germain (on Tuesday), they asked the same to Luis Enrique. He said the difference is that Arsenal have had the same manager for five years, (PSG) are one year and a half.
"We are three months. It's a huge difference. I'm really convinced that we cannot compete with that club. The target is to improve and slowly, slowly go close to them. But we are not in this moment ready for that."
What is the current state of play?
As it stands, Chelsea only sit one point adrift of Arsenal and Man City, with Liverpool two points clear of the West Londoners at the top.
In all competitions, though, Chelsea have recorded five victories in a row, scoring a total of 17 goals during that period.
The one downside has been two goals being conceded in each of the most recent wins over Brighton & Hove Albion and Gent respectively.