The Swansea City captain was unbelievably influential as his side moved away from the drop zone to secure a mid-table finish, and he will be looking to use the same passion and determination to lead his country to success in France.
"I think he's massively important," Chester told the South Wales Evening Post, with him expected to start in the heart of defence alongside Williams this summer.
"He's shown during his time at Swansea just how important he can be."
The West Bromwich Albion man continued, saying that you can "see the leadership" in the Wales skipper, especially when he doesn't play as he's always "certainly missed.
"Defensively, he's no nonsense and away from the pitch he's a very loud character and someone that brings everyone together."
The Dragons will be looking for him to unite the team once more in France, having done so with great success in qualifying to lead the nation to their first major tournament for 58 years.
His ability to bring the group together, along with manager Chris Coleman, has seen a strong work ethic and great organisation get them to the Euros, without the need for huge names - with Gareth Bale's presence simply a bonus.
Wales will hope Williams continues to be "a huge presence on the pitch" this month, while Chester is looking to continue the "good relationship" they have to keep the team's Group B opponents at bay.
Can Williams influence a potential switch?
These comments come amidst a heap of speculation regarding Chester, who has been linked with a move to Swansea since the turn of the year.
The Baggies' defender has been granted little playing time at the Hawthorns this season, and it almost cost him his place on the plane to France.
It's understandable that he's assessing his options heading into the summer then, and with him well aware of Swansea's January interest, they just might be an option he's wanting to explore.
"There was interest from Swansea in January," he was quoted by ClubCall as saying, with West Brom rumoured to have declined an £8 million bid from the South Wales club at the beginning of the year.
However, they opted not to sell as Chester had only been at the club for six months, he explained, as well as them being "reluctant to sell [him] to another club in such a similar position in the league."
After Christmas, the Welshman got a few more games under his belt, but admitted that it was still "frustrating" as he wasn't been deployed in his favoured position; settling for a spot at full-back and not in the centre of defence.
"I'm not sure what the stance is right now," Chester said regarding the Baggies' opinion on letting him go.
However, he knows what his stance is, saying: "I feel I'm good enough to play every week in the Premier League."
Whether he will get that at the Hawthorns or have to look elsewhere for football, remains to be seen.