COOK IT.
Grill the oiled lemon slices over direct heat (the hotter side of your grill) for 3 minutes, turning once until you see those beautiful charred grilled marks. Transfer to a plate.
Next, place your chicken on the cooler side of the grill. Let it cook about 15-20 minutes until the surface is browned and starting to crisp.
Turn the chicken over, close the lid, and continue grilling about 8–10 minutes more, until a meat thermometer registers 160°F at the thickest part of the breast.
This step is optional, but totally encouraged. If you like your chicken with a little char on the surface, open your grill and transfer them to the hotter side. It should only take a minute or two over direct high heat to get the results you want.
Transfer chicken breasts to a cutting board and let rest 10–15 minutes.
This is where it all comes together. Place your chicken breasts on a plate or platter. You can cut them into slices or leave them intact. Scatter with thyme sprigs, olives, grilled lemon slices, and reserved fresh lemon slices over the chicken. Drizzle the plate with reserved lemon juice and remaining ½ cup oil over. Let all those flavors sit with each other for a few minutes, and then dig in!