Prepare the chicken by seasoning both sides with salt, pepper, and dried oregano.
In a large skillet over medium heat, add olive oil and heat until shimmering.
Place the seasoned chicken breasts into the skillet and cook for about 5-7 minutes on each side, or until they are golden brown and cooked through. Remove the chicken and set aside.
In the same skillet, add the sliced onion and diced bell peppers. Sauté for about 3-4 minutes until they begin to soften.
Add the minced garlic and cherry tomatoes to the skillet and cook for another 2-3 minutes until the tomatoes start to burst.
In a small bowl, mix together balsamic vinegar, honey, salt, and black pepper. Pour this mixture into the skillet, allowing the flavors to combine.
Return the chicken to the skillet, and add the baby spinach. Spoon some of the balsamic mixture over the chicken.
Cover and cook for an additional 5 minutes, letting the spinach wilt and the sauce thicken slightly.
Serve warm, garnished with fresh basil leaves if desired.