Season the chicken breast with half of the sea salt and black pepper.
Heat a non-stick skillet over medium heat and cook the chicken for 6-7 minutes per side until the internal temperature reaches 165°F.
While chicken cooks, bring a pot of salted water to a boil and cook the gnocchi until they float to the surface, about 2-3 minutes.
Drain the gnocchi and set aside, reserving 1 tablespoon of the pasta water.
In a small food processor, combine the baby arugula, extra virgin olive oil, garlic clove, lemon juice, and grated parmesan cheese.
Pulse the mixture until a smooth, vibrant green pesto forms, adding the reserved pasta water if a thinner consistency is desired.
Remove the chicken from the skillet, let it rest for 3 minutes, then slice into thin strips.
In the same skillet, add the cherry tomatoes and sauté for 2 minutes until they are softened and just beginning to burst.
Return the gnocchi and chicken to the skillet, pour in the arugula pesto, and toss gently over low heat until everything is well combined and warmed through.