Heat a large skillet over medium-high heat with a drizzle of olive oil. Add the chopped marinated chicken and cook for 6 to 8 minutes, stirring occasionally, until browned and cooked through to 165°F. Remove and set aside.
In the same skillet add another tablespoon of olive oil or butter. Add the gnocchi straight from the package and sauté for 2 to 3 minutes until golden on the outside.
Add 1/4 cup water or chicken broth, cover, and cook for another 3 to 5 minutes until the gnocchi is tender. If any liquid remains let it cook off uncovered.
Reduce the heat to low. Add the heavy cream, pesto, and lemon juice. Return the chicken to the skillet. Stir everything together and simmer gently for 2 to 3 minutes.
Stir in the Parmesan until melted and the sauce is creamy. Add a splash of cream or broth if it gets too thick.
Taste and adjust lemon, salt, and pepper as needed. Finish with extra Parmesan, fresh lemon zest, and cracked black pepper. Serve immediately.