Preheat oven to 350 degrees F.
Season the chicken liberally with salt, pepper and garlic powder. Dredge the chicken breasts in the flour, shaking off excess. In a bowl add ½ cup of the pesto. Using your hands generously apply the pesto all over the chicken.
Heat 1 tablespoon of the butter and 2 tablespoons of olive oil in a large oven safe skillet over medium high heat. Add the chicken and cook for 2 minutes per side, until browned but not cooked through. Set the chicken pieces aside on a plate.
Into the same pan, add the remaining 4 tablespoons butter over medium high heat. Add the heirloom tomatoes and cook until the tomatoes begin to burst, about 5 minutes. With a wooden spoon, gently crush the tomatoes to release their juices and bump up the heat to high, stirring often for 1-2 minutes. When all the tomatoes have burst, bring the heat back down to medium and add the onion. Cook for 3-5 minutes, or until the onion becomes soft and translucent. Add salt, pepper and garlic powder to taste. Add the zucchini, and cook for an additional 3 minutes, stirring often.
Next, add the white wine and bring to a simmer. When the wine reduces to about half, take the veggies off the heat and arrange the chicken pieces over the top. Transfer the oven safe skillet to the preheated oven and bake for 15-20 minutes, or until the chicken is cooked through.
When ready to serve swirl the remaining ¼ cup pesto around the pan, top with fresh parmesan cheese and enjoy!