Heat a grill to medium high.
Cut into and across chicken but not all the way through. Pound out a bit then season inside with salt and pepper. Combine the pasted garlic with lemon zest and thyme, and divide among the chicken. Spread chicken with mustard and fill with ham and cheese, close chicken up, drizzle liberally with olive oil and season the skin and backside of breasts with salt and pepper. If the chicken seems overstuffed, secure with wet skewers or twine.