The Borussia Dortmund attacker joined Chelsea in a £58 million ($73m) deal on Wednesday, although he was immediately loaned back to BVB for the remainder of the 2018-19 season.
Some have questioned whether the 20-year-old Pulisic is ready for the move to the Premier League after losing his starting berth at Dortmund to Jadon Sancho, but Chandler has little doubt his compatriot is ready to shine at the highest level.
"Pulisic has the abilities to play on the biggest stage," Chandler told Goal and DAZN ahead of Frankfurt's US tour.
"But like other young players, he will have to prove himself in every game and always work hard. If he does just that, he can achieve some big things."
Pulisic is the key exponent of a new generation of players looking to lead the way for the national team after they missed out on qualification for the 2018 World Cup in Russia and Chandler is optimistic over the way the game is developing in the USA.
"Missing the World Cup was very unlucky, a major setback," he added.
"But I have little doubt the USA will bounce back and qualify for the next tournament. American soccer has so much potential, the possibilities are endless. Especially when it comes to developing players. MLS continues to develop as well. In the future, it will not just be high-profile names who are past their best, but also players who came through youth academies and made their way up. That's the way it should be.
"Over the last five to six years, soccer has become more important in the USA, mainly thanks to Jurgen Klinsmann. He did a lot for soccer, changed a lot of things and worked hard to make the sport more popular. His life was all about football. We travelled a lot within the country and tried to play as many games as possible in different places and organise training camps to be close to the fans."
Being born in Frankfurt, Chandler has spent his entire soccer career in Europe, but the wing-back could very well see himself make the move to MLS at some point in the future.
"I want to stay in Germany for a few more years, but maybe I could move to MLS toward the end of my career," the 28-year-old concluded.