Season the chicken breast with half of the sea salt and black pepper.
Heat a non-stick skillet over medium-high heat and sear the chicken until golden brown and cooked through, about 6 minutes per side.
While chicken cooks, bring a small pot of salted water to a boil and cook the gnocchi until they float to the surface, then drain and set aside.
In a food processor, combine the baby arugula, walnuts, parmesan cheese, garlic, lemon juice, and olive oil, pulsing until a smooth pesto forms.
Remove the chicken from the skillet and let it rest for 3 minutes before slicing into bite-sized pieces.
In the same skillet, add the cherry tomatoes and sauté for 2 minutes until the skins begin to blister.
Add the cooked gnocchi, sliced chicken, and arugula pesto to the skillet, tossing everything together until well-coated and heated through.