The versatile defender is in and out of the first team at present, but is hoping for more game time under new boss Graham Potter.
Chalobah was speaking after his side's routine win in the Champions League group stages over AC Milan.
"I am at Chelsea, this is my club," he stated.
"Every time I get the chance I want to show the manager that I am good enough to play. Any chance I get I need to do my best and let the manager decide. [Potter] said I have been training well so take it into the game. He knew I was ready and what I could do.
"Playing at a big club like Chelsea, you've got to be ready. If you are not playing you need to know what you need to do better. It starts in training. I've been ready for a couple of games now and I got my chance today and hopefully, I can take it.
"I felt good stepping on the pitch today. It has been a long time but it felt good and I can't wait for the next game."