In a food processor, combine the baby arugula, parmesan cheese, pine nuts, garlic, and lemon juice, pulsing until a coarse paste forms.
Slowly drizzle in the extra virgin olive oil while the processor is running until the pesto is smooth and vibrant.
Season the chicken breast with half of the sea salt and black pepper, then sear in a non-stick skillet over medium-high heat for 6 minutes per side until golden and cooked through.
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 immediately.
Remove the chicken from the skillet to rest, then add the halved cherry tomatoes to the same pan, sautéing for 2 minutes until they begin to blister.
Slice the rested chicken into bite-sized strips.
In a large bowl, toss the warm gnocchi, blistered tomatoes, and sliced chicken with the arugula pesto until thoroughly and evenly coated.