Place the cut chicken strips in a mixing bowl and add about half of the Asian BBQ sauce; toss to coat evenly.
Cover and refrigerate the chicken for 45 minutes to marinate.
While the chicken marinates, rinse the brown rice under cold water until the water runs clear.
Combine the rinsed rice, 2 1/8 cups water and a pinch of salt in a medium pot; bring to a boil, then reduce heat to low, cover, and simmer for 30–40 minutes until the rice is tender and water is absorbed.
If using wooden skewers, soak them in water for 10–15 minutes to prevent burning; thread each marinated chicken strip onto skewers.
Preheat a grill or grill pan to medium-high heat. Grill the skewers 3–5 minutes per side, turning once, until the chicken is cooked through and reaches an internal temperature of 165°F (74°C).
Serve the grilled skewers over the cooked brown rice and spoon the remaining Asian BBQ sauce over the chicken and rice.