The 25-year-old Brazilian midfielder joined the Blues from Anzhi Makhachkala for around £25.5m during the summer transfer window.
"I know that I haven't secured my spot here," Willian told Globo Esporte. "I'll do my best to achieve that place, while respecting the other players. I'll train, play and do my best to get the trust of the manager and of the fans."
Willian has signed a five-year contract at Stamford Bridge.