The Brazilian playmaker was among those acquired by Jose Mourinho over the summer, with big money paid to secure his services from Anzhi Makhachkala and keep rival interest at bay.
Willian has had to be patient in his pursuit of regular football at Stamford Bridge, with his first Premier League outing coming at Norwich City on Sunday.
He marked the occasion with his first goal for the Blues - wrapping up a 3-1 win - and the 25-year-old says there is plenty more to come from him now that he is up and running.
Willian told Globo Esporte: "I am very happy to have made my Premier League debut this way.
"I did well off the bench, doing what Mourinho asked me to do. I managed to start the move that led to the second goal and then I scored the third goal.
"It was very exciting and I am not only happy for the goal, but also for the win - which was important for our team.
"I am slowly recovering my best form, gaining match fitness.
"I will try to do my best whenever I have the opportunity to play. I intend to grow with each match."