In small bowl, whisk orange zest and juice, lime zest and juice, soy sauce, brown sugar or honey, garlic and ginger. While whisking, slowly add vegetable or other neutral oil until emulsified. Whisk in sesame oil and dash of hot sauce, if using.
Pour marinade over chicken in glass baking dish or zip-top bag. Refrigerate at least 1 hour (up to overnight).
When ready to cook, oil grill grates or cool with nonstick cooking spray, then preheat to medium-high heat.
Remove chicken from marinade and pat dry; discard marinade. Grill 5 minutes per side, then continue flipping every few minutes until cooked through, about 12 minutes for thighs and 16 minutes for breasts (safe internal temp. 165°F).
Remove chicken from grill and let rest 5-10 minutes. Slice across the grain, if desired. Serve, refrigerating any leftovers.
