Season the chicken breasts with salt pepper and half the oregano. Warm 1 tablespoon olive oil in a large skillet over medium-high heat and cook the chicken for about 6 to 7 minutes on each side until golden and cooked through. Transfer the chicken to a plate and let it rest.
Add the remaining olive oil to the same pan and sauté the chopped red onion until soft, about 2 to 3 minutes. Stir in the minced garlic and cook for an additional 30 seconds until aromatic.
Include the diced bell pepper and zucchini in the pan and cook for 3 to 4 minutes until they start to soften. Add the orzo pasta and toss it with the vegetables and oil.
Pour in the chicken broth and bring the mixture to a gentle boil. Lower the heat to medium-low, cover the pan, and simmer for 10 to 12 minutes, stirring once in a while, until the orzo absorbs most of the liquid and becomes tender.
Slice the rested chicken into strips. Fold in the halved cherry tomatoes, balsamic vinegar, and remaining oregano. Gently combine the chicken slices and cook for 2 to 3 more minutes until the tomatoes are warmed and a light glaze forms from the balsamic.
Take the pan off the heat, sprinkle fresh basil over the top, and serve immediately while hot.
