Whisk together the lemon juice, olive oil, salt, pepper, and thyme. Pour over the chicken breasts in a large bowl. Cover and marinate in the refrigerator for 6 hours or overnight. (The longer the chicken marinate, the better it will taste).
Heat the grill and cook the chicken breasts for 10 minutes on each side, until just cooked through.
Remove from the grill, cover and let stand for a couple of minutes before serving.
Cook the olive oil, sesame oil, red onion, garlic, ginger root, and red pepper flakes in a small, heavy bottomed pot on medium heat until the onion is transparent, 10 to 15 minutes.
In a bowl whisk in the vinegar, sugar, soy sauce, peanut butter, ketchup, sherry and lime juice.
Add to the onion mixture and cook for 1 minute.
Cool and use alongside the chicken.