Whisk sugar, oil, mustard, vinegar, garlic, lemon juice, lime juice, and salt together in medium bowl until blended to make marinade.
Pour into resealable plastic freezer bag. Add chicken; seal bag. Turn several times to completely coat pieces. Refrigerate at least 2 hours or overnight turning occasionally. When ready to cook, remove chicken from bag, allowing excess marinade to drip off. Discard leftover marinade.
Spray cold grill and cooking tongs well with PAM(R) for Grilling Cooking Spray. Position grill 4 to 6 inches from heat. Heat grill according to suggestion by manufacturer. Cook chicken over medium heat 15 to 35 minutes** or until juice is no longer pink in thickest part; turn frequently to prevent burning.
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*Works well with skin on or off.
**Cooking Time Guidelines: boneless, skinless chicken breasts should take 15-20 minutes; bone-in breasts will take about 20-25 minutes; dark meat may take up to 35 minutes.