In a food processor, combine the garlic, chiles, shallots, ginger and turmeric and pulse until finely chopped. Add the 1/4 cup of vegetable oil and pulse to a fine paste. Transfer the paste to a small skillet and cook over moderate heat, stirring, until fragrant and lightly browned, about 5 minutes. Let the paste cool completely and season with salt and pepper.
Set the chicken in a baking dish and rub the paste all over it. Place the bay leaves on top. Cover and refrigerate for at least 4 hours or overnight.
Light a grill. Line the grate with a double sheet of heavy-duty aluminum foil brushed lightly with oil. Transfer the chicken to the foil, skin side up. Cover and grill over moderate heat (350° to 375°) for 1 hour, until nearly cooked through. Add the limes to the foil and grill the chicken until the juices run clear when an inner thigh is pierced, about 15 minutes longer. Carve the chicken, transfer to a platter and serve with the limes.