Heat 1 tablespoon olive oil over medium heat. Add the chicken, sprinkle with ¼ teaspoon salt, and saute until browned and cooked through, about 10 minutes. Remove from the pan and set aside.
To the same pan, heat an additional 1 tablespoon olive oil and the garlic. Saute over medium-low heat for 1 minute until lightly golden, stirring frequently.
Turn the heat to medium and add the tomatoes, 2 tablespoons olive oil, the vinegar, ½ teaspoons salt, and the zoodles, stirring to combine.
Add the cooked chicken and cook everything together on medium heat for 1-2 minutes, or until the zoodles are just tender, being careful not to overcook.
Serve warm, sprinkled with basil and freshly ground pepper.