Make the marinade. In a bowl, whisk together the soy sauce, fish sauce, brown sugar, tamarind paste, peanut butter, lime juice, garlic, ginger, and oil until smooth.
Marinate the chicken. Add the chicken pieces and toss until well coated. Cover and refrigerate for at least 30 minutes, or up to 4 hours.
Prepare the skewers. Thread the chicken onto skewers, leaving a little space between each piece so the heat can circulate.
Grill the chicken. Heat a grill or grill pan over medium-high heat. Cook the skewers for about 10 minutes, turning occasionally, until the chicken is cooked through and slightly charred on the edges.
Serve. Transfer to a platter and top with chopped peanuts, red chilies, and cilantro. Serve with lime wedges for squeezing over the top.