In a medium bowl, whisk together the olive oil, lemon juice, lemon zest, minced garlic, sea salt, black pepper, and dried oregano to create the marinade.
Cut the chicken breast into 1-inch cubes and add them to the marinade along with the peeled and deveined shrimp, tossing well to coat.
Cover the bowl and let the proteins marinate in the refrigerator for 15 to 20 minutes.
While the proteins marinate, chop the red bell pepper, zucchini, and red onion into uniform chunks suitable for skewering.
Preheat your grill or a cast-iron grill pan over medium-high heat.
Thread the marinated chicken, shrimp, and vegetables onto skewers, alternating ingredients for a colorful presentation.
Place the skewers on the hot grill and cook for 3-4 minutes per side, or until the chicken is cooked through and the shrimp are pink and opaque.
Remove from the heat and serve immediately while the vegetables are tender-crisp and the meat is juicy.