Toss the chicken, onion, and zucchini with teriyaki sauce. Marinate for a few hours or overnight for best flavor.
In a 9x13-inch baking dish, combine the rice, water, olive oil, and salt.
Thread the chicken and vegetables onto skewers and lay them across the baking dish so they hang over the rice.
Cover with parchment paper and foil. Bake at 375°F for 25 minutes.
Remove the cover, baste with remaining teriyaki sauce, and bake 10 minutes more.
Broil for 3-5 minutes if desired.
While the chicken bakes, toss all cucumber salad ingredients together.
Serve over the fluffy jasmine rice with the cucumber salad on the side.
