Combine ginger, garlic, sambal oelek, lime juice and vegetable oil in a mini chopper or by hand and process until well combined. Pour over chicken and marinate, covered, for 2 hours in the refrigerator.
Soak bamboo skewers in water for 30 minutes.
Preheat grill to high.
Thread one piece of chicken onto each skewer and grill for 2 to 3 minutes per side, turning once, or until cooked through. Serve the chicken satays with Thai dipping sauce.
Whisk together garlic, sambal oelek, ketchup, fish sauce, water, lime juice and brown sugar. Stir in carrot and mint. Makes about 1 cup (250 ml).