Whisk together all ingredients except chicken in a large bowl.
Lay out a piece of heavy plastic wrap on a cutting board. Flatten out several chicken thighs on top of it, then cover with another piece of plastic wrap.
Use a meat mallet, rolling pin, or heavy skillet to pound the chicken as thin and even as you can get it. After all the chicken is pounded, cut each chicken thigh in half lengthwise.
Add chicken to marinade and turn to coat all sides. Marinate at room temperature for 30 minutes, or in the refrigerator up to overnight. Return to room temperature before grilling.
If using bamboo skewers, soak in water for at least 30 minutes. Thread chicken pieces onto skewers.
Heat grill or grill pan to medium-high for 5 minutes.
Grill 4-5 minutes per side, turning once. If you put a lot of meat onto a skewer, it will take longer to cook. If you use more skewers and have the meat more stretched out, it will cook more quickly.
Serve immediately with Thai cucumber salad and spicy Thai sunflower seed sauce.