Preheat the oven to 400°F. Place the chicken breasts on a baking sheet covered with parchment paper or lightly oiled, brush with extra virgin olive oil and season with salt and cracked black pepper. Bake in the oven for 15 minutes.
Take the chicken out of the oven to add the tomatoes on the vine, again brushing with oil. Return to the oven and bake for an additional 15 minutes, or until the chicken is lightly browned and cooked through.
Meanwhile, prepare the pesto by blending together all the pesto ingredients except the olive oil in a food processor or blender. Once a paste has formed, slowly add the oil as the processor/blender is running. Stop once the pesto is well combined and reaches the desired consistency.
To create your pasta, spiralize the zucchini. Alternately, you can use a vegetable peeler to make zucchini ribbons.
In a skillet with a very small amount of olive oil (just enough to keep them moist and prevent sticking), sauté the zucchini for 3 minutes or until softened. Remove from heat and stir in the pesto until blended.
Assemble the dish by placing an equal amount of the pesto zucchini per each chicken serving in a bowl. Top with sliced chicken, baked tomatoes, and a fresh basil garnish.