In a large microwave-safe bowl, add sliced onions and bell peppers. Cook on high in a microwave for about 5-8 minutes, until soft.
In the meantime, Add chicken pieces to a plate. Squeeze the juice of 1 lemon over chicken. Sprinkle 1 teaspoon minced rosemary and add a little salt and pepper.
Coat a large, nonstick pan with cooking spray. Add 1 teaspoon of olive oil and heat. Add chicken and juice from the lemon into the pan. Cook until no longer pink, about 5-6 minutes. Stir often. Remove chicken to a plate.
In the same pan, coat again with cooking spray. Add 2 teaspoons olive oil. Add cooked onions and bell peppers, basil, and a little salt and pepper. Pour ¼ cup balsamic vinegar over the top. Cook over medium-high heat, stirring often, until the vegetables are soft and slightly caramelized, about 10 minutes. If the pan gets too dry, add 1 more teaspoon of olive oil and 3 tablespoons of water. Stir in garlic and cook, stirring, until fragrant and soft, 1 minute. Return chicken to pan. Add 2 tablespoons balsamic vinegar and 1 tablespoon rosemary. Mix everything together. Continue to cook, stirring until warmed and well blended, about 2 minutes.
Arrange on a platter or plate each serving. Any leftovers will keep in the fridge a few days or freeze great!