Bring a medium pot of salted water to a boil and cook the potato gnocchi according to package instructions until they float, then drain and set aside.
In a small food processor, combine the baby arugula, walnuts, parmesan cheese, lemon juice, half of the garlic, and 1 teaspoon of olive oil, pulsing until a coarse pesto forms.
Dice the chicken breast into bite-sized pieces and season with sea salt and black pepper.
Heat the remaining 1 teaspoon of olive oil in a large skillet over medium-high heat and sear the chicken until golden brown and cooked through, approximately 5-7 minutes.
Add the cherry tomatoes and the remaining minced garlic to the skillet, sautéing for 2 minutes until the tomatoes begin to soften and blister.
Reduce the heat to low, add the cooked gnocchi and the arugula pesto to the skillet, and toss everything together until well-coated and heated through.
Serve immediately, garnished with an extra pinch of black pepper if desired.