Preheat your oven to 400°F and toss the cherry tomatoes with half the olive oil and a pinch of sea salt on a baking sheet.
Roast the tomatoes for 10-12 minutes until they are blistered and beginning to burst.
Season the chicken breast with the remaining sea salt and black pepper, then sear in a pan over medium-high heat with the remaining olive oil until cooked through, about 6 minutes per side.
While the chicken cooks, bring a pot of salted water to a boil and cook the gnocchi until they float to the surface, then drain, reserving two tablespoons of the cooking water.
In a small bowl, whisk together the basil pesto and Greek yogurt with the reserved pasta water to create a creamy sauce.
Slice the cooked chicken into bite-sized pieces and return them to the pan along with the minced garlic, sautéing for 1 minute until fragrant.
Add the cooked gnocchi, roasted tomatoes, and the creamy pesto sauce to the pan, tossing gently to coat everything evenly.
Garnish with fresh basil leaves and serve immediately while warm.