Chavez will start to appear after fighting the unexpected siege at your base that Nat or Santos brings. They lost their home due to a plague heart taking over.
You can find him North-West of the Plane Crash Site
The West Marshal Road that leads to the West Destroyed Bridge
West of Spencer's Mill
I provided these locations as a keypoint of where you can find him. His spawn is only at one location.
He will call out in the radio and hoping for someone to help him, you arrive and are tasked to help him find a plague cure as he is infected. If you do so happen to have a Plague Cure, you can give it to him and recruit him right then. If you do not happen to have a Plague Cure, you will head South towards the Red Talon Outpost(Military Site) to give to him.
When you give him the Plague Cure, you will be tasked to Escort him Home.