The competition for places is strong at Stamford Bridge this season after a number of expensive acquisitions over the summer.
But Hudson-Odoi was able to make a mark against Rennes on Tuesday, scoring in the 2-1 victory.
"Every game that you play you want to go out there and give your best," the 20-year-old said after the game.
"I think that everybody's playing really well at the moment and we want to keep improving, keep working hard and keep our momentum going.
"So every opportunity I get I just want to take it, hopefully keep getting goals, getting assists for the team, working hard for the team. But really I am happy that we got the three points and we won the game."