Brush the cooking grates clean. Grill the chicken cutlets, cheese side down first, over direct medium-high heat, with the lid closed, until the chicken is cooked through and the ham begins to brown, 6 to 8 minutes, turning once after 3 minutes. To check for doneness, cut into the underside of one breast. The meat should be opaque all the way to the center. Remove from the grill and let rest for 3 to 5 minutes.
Brush the cooking grates clean. Grill the chicken cutlets, cheese side down first, over direct medium-high heat, with the lid closed, until an instant-read thermometer inserted into the thickest part of the chicken registers 165°F, and the ham begins to brown, 6 to 8 minutes, turning once after 3 minutes. Remove from the grill and let rest for 3 to 5 minutes.
Brush the cooking grates clean. Grill the chicken cutlets, cheese side down first, over medium-high heat, with the lid closed, until the thickest part of the chicken registers 165°F, and the ham begins to brown, 6 to 8 minutes, turning once after 3 minutes. Remove from the grill and let rest for 3 to 5 minutes.