Prepare the pesto by pulsing the arugula, walnuts, parmesan, lemon juice, and garlic in a food processor until finely chopped and combined.
Season the chicken breast with half of the sea salt and black pepper.
Heat the olive oil in a large skillet over medium heat and sear the chicken until golden and cooked through.
Remove the chicken from the pan, let it rest for a few minutes, then slice into bite-sized pieces.
Boil the potato gnocchi in a pot of salted water according to the package instructions until they float, then drain.
In the same skillet used for the chicken, add the cherry tomatoes and sauté for 2 minutes until they begin to blister and soften.
Add the cooked gnocchi, sliced chicken, and prepared arugula pesto to the skillet with the tomatoes.
Toss everything together over low heat for 1 minute to ensure the meal is evenly coated and warmed through before serving.