Season chicken pieces with 1/2 teaspoon salt and black pepper. Heat olive oil in a large, deep skillet over medium-high heat. Add chicken and cook 5-6 minutes until browned and cooked through. Transfer to a plate.
In the same skillet, add garlic and sun-dried tomatoes. Cook for 1 minute until fragrant, stirring frequently.
Add gnocchi, chicken broth, heavy cream, Italian seasoning, and remaining 1/2 teaspoon salt to the skillet. Bring to a simmer, then reduce heat to medium and cook for 8-10 minutes, stirring occasionally, until gnocchi is tender and sauce has thickened.
Stir in Parmesan cheese until melted and combined. Add spinach and cook for 1-2 minutes until wilted.
Return cooked chicken to the skillet and toss everything together. Serve immediately with additional Parmesan cheese if desired.