If using bamboo skewers, soak them in water for 20 minutes. Preheat an outdoor grill or grill pan to medium-high heat, about 400°F to 450°F (205°C to 230°C). Clean and oil the grates well.
In a medium bowl, whisk together the vinegar, calamansi or lime juice, soy sauce, brown sugar, ginger, garlic, lemongrass, salt, pepper, and 1 tablespoon annatto oil. Pour 1/4 cup (60 ml) of this clean marinade into a small bowl and set aside for basting.
Add the chicken to the remaining marinade and toss until coated. Let stand for 15 minutes at room temperature, or refrigerate for up to 2 hours for deeper flavor. Do not marinate longer than 4 hours because the acidic mixture can affect the chicken's texture.
Thread the chicken pieces onto the skewers, leaving a little space between pieces so they cook evenly. Discard the marinade that touched the raw chicken.
Grill the skewers for 10 to 14 minutes, turning every 3 to 4 minutes, until browned in spots and the thickest pieces reach 165°F (74°C) on an instant-read thermometer. Brush lightly with the reserved clean marinade during the final few minutes of cooking.
Brush the hot skewers with the remaining 1 tablespoon annatto oil. Rest for 3 minutes, then serve with lime wedges and scallions if desired.