In a medium bowl whisk the marinade ingredients. Cut the chicken thighs into 1-½-inch pieces. Cut each zucchini lengthwise in half, and then cut each half crosswise into 1-inch pieces. Add the chicken thigh pieces and the zucchini pieces to the bowl with the marinade and turn to coat them thoroughly. Cover and refrigerate for 2 to 4 hours.
If using bamboo skewers, soak in water for at least 30 minutes.
Prepare the grill for direct cooking over medium heat (350°F to 450°F).
Meanwhile, prepare the rice. In a medium saucepan over medium-high heat, warm the oil. Add the onion and garlic and cook until they start to soften, about 2 minutes, stirring occasionally. Add the bell peppers and cook for 2 minutes. Add the rice and cook for 1 minute, stirring occasionally. Pour in the broth, add the salt, and bring to a boil. Cover, reduce the heat to low, and simmer very gently until all the liquid has been absorbed, about 20 minutes. Remove from the heat and stir in the parsley. Keep warm.
Thread the chicken pieces and the zucchini pieces alternately onto skewers. Brush the cooking grates clean. Grill the kabobs over direct medium heat, with the lid closed as much as possible, until the meat is firm to the touch and the juices run clear, 8 to 10 minutes, turning once or twice. Remove from the grill and let rest for 3 to 5 minutes. Serve the kabobs warm over the rice.