The Blues remain unbeaten under Thomas Tuchel and reached the quarter-finals of Europe's top competition with an impressive victory over Atletico Madrid.
Chelsea are also preparing for an FA Cup semi-final with Manchester City and Chilwell has confidence that they can make it a season to remember.
Asked if the club can win two pieces of silverware this term, he said: "It’s 100 per cent possible. We’re in both competitions and playing well, but it’s not something we’re talking about.
"I think it’s in the back of everyone’s minds but at the moment – I know it’s cliched – we’re just taking it week by week and the manager’s indicated to us what we need to do.
"We have to keep improving in training and going into every match with the same mindset that we have been."
Chilwell has faced renewed competition from Marcos Alonso for his place in the team but believes that the threat of losing his place has lifted his performances.
He said: "I’m working hard in training and, coming into games, I’m asking a lot of questions, where I can be positionally, so I can improve and get more opportunities to play in that role.
"But on the other side of things when you’ve got two or three players in each position that can do different roles and have different strengths, it makes everyone train a lot harder, which is creating a good buzz around the place."