The highly-rated Scot has become the latest teen sensation to make a positive impression in English football.
Big things have been expected of him for some time, with those at Stamford Bridge having moved to lure him away from Rangers in 2017.
Gilmour is now flourishing on a senior stage, with a man-of-the-match performance in a cup clash with Liverpool having been followed by another against Everton in league competition .
He has benefited from the misfortune of others, with an untimely suspension for Italy international Jorginho opening a first-team door to the promising academy graduate.
Gilmour has grabbed his opportunity with both hands and, having shown Frank Lampard what he is capable of, is looking forward to seeing many more minutes over the coming weeks.
"They help me a lot with their movement so I can play them the ball. You need to keep it moving, keep it simple. Then when you start to settle into the game you can start hitting the longer passes and play more forward passes.
"It's down to the gaffer as well for trusting me to play in these big games. Jody, Joe and the gaffer have been brilliant with me. I have had them [Morris and Edwards] through the youth and then to come to the first team with them has been really good for me. It's really good for them to show trust.
"You can see that the manager will give the young players an opportunity and it's up to us to take it when we get the chance. It's exciting to be at Chelsea and I just want to take my opportunity when it comes."
The last week has been something of a whirlwind for Gilmour, as he has burst onto a global scene, but he is looking to take everything in his stride and enjoy the moment.
He added on making a first Premier League start against the Toffees : "It was amazing. It was a dream come true to make my full Premier League debut, but most of all getting the win was just fantastic.
"I was more excited than nervous to be fair. It was tough. I just wanted to work my hardest, play well and do my best for the team.
"I'm just delighted to help the team get the win and that we came out on top. I enjoyed the game, especially off the back of a good win against Liverpool in midweek, and hopefully I can get another chance to play. I'm loving it around here at the minute, it's brilliant."
Chelsea will be back in action on Saturday when they take in a trip to Aston Villa.