Begin by marinating the chicken breasts. In a bowl, combine half the olive oil, the juice and zest of the lemon, minced garlic, salt, pepper, and oregano. Add the chicken and coat well. Let it rest while preparing the vegetables.
Slice the zucchini and squash into approximately ¼-inch thick rounds, keeping them uniform for even grilling. Arrange on a tray or plate for easy access.
Preheat your grill or grill pan over medium-high heat. Brush it lightly with the remaining olive oil to prevent sticking.
Grill the chicken breasts for about 6-8 minutes per side, until fully cooked and golden brown with visible grill marks. Adjust cooking time based on thickness.
While the chicken cooks, place the sliced zucchini and squash onto the hot grill. Cook for approximately 3-4 minutes per side until they develop grill lines and become tender and slightly caramelized.
Remove the cooked chicken and vegetables from the grill. Let the chicken rest for a few minutes to retain its juices, then slice it if desired.
Transfer the grilled zucchini and squash to a serving platter. Squeeze fresh lemon over the vegetables and drizzle with a splash of olive oil for added brightness.
Arrange the sliced grilled chicken alongside the vegetables. Garnish with additional lemon zest or herbs if desired.
Serve the dish warm, enjoying the vibrant flavors and textures in each bite.