For the chicken:
Whisk together the lemon juice, olive oil, salt, pepper, and thyme. Pour over the chicken breasts in a nonreactive bowl. Cover and marinate in the refrigerator for 6 hours or overnight.
Heat a charcoal grill. Grill the chicken breasts for 10 minutes on each side, until just cooked through. Cool slightly and cut diagonally in 1/2-inch-thick slices. Skewer with wooden sticks and serve with Satay Dip.
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. Whisk in the vinegar, brown sugar, soy sauce, peanut butter, ketchup, sherry, and lime juice; cook for 1 more minute. Cool and use as a dip for Grilled Lemon Chicken skewers.
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