Chas became a (half-)angel after his death.
In the film's official novelisation we see him twice after his death, firstly welcoming Isabel to heaven;
Things were accomplished, in that pause, after Satan said, Fine.
A spirit was released from Hell - and found itself in Heaven, where there was celebration at her arrival, and many things came clear to her at last....
"Welcome, Isabel," said her grandmother. "Welcome, my darling. I'd like you to meet some friends of mine - and I don't think you ever met your grandfather.... Oh - and here's a friend of a friend. His name is Chaz.... "
and later he is described as heaven's newest half-angel (e.g. a mortal soul granted angelic powers) returned to Earth:
Behind them, Gabriel shuddered, sensing the opening of a doorway...
And the room filled with light. A silhouetted figure appeared, in a shimmering doorway. Heaven illuminated behind him with higher-dimensional clarity. Heaven's newest half-angel: It was Chaz, adjusting his cap, casually. Smiling sardonically at Gabriel. "S'up, Gabie."
Chaz robbed his hands together. He had a lot of work to do in his new gig, and he was looking forward to it. "P.S., man," Chaz said to Gabriel, walking past him. "You have one shitload of explaining to do."
Although the localisation is slightly different (he rises in the hospital, not the graveyard), this would seem a solid explanation for his return.