Chester still has work to do to return to match action, but his return to the training pitch comes as positive news.
Marvelous Nakamba, meanwhile, could make his Premier League bow against West Ham on Monday.
Jonathan Kodjia and Matt Targett, though, are likely to miss the game.
"James Chester trained for the first time again this week," said Smith.
"He's been out since the Shrewsbury game in pre-season, so his rehabilitation will take longer.
"But he's in and around us now.
"As for Marvelous, he's close to being ready. He's looking good.
"Unfortunately, (Kodjia) picked up an innocuous head injury, which we're assessing at the moment. We'll see how he is.
"Targett will probably be looking at the Arsenal game. I think Monday will come too quickly for him."