Heat the olive oil in a large skillet with a lid over medium heat, and cook and stir the chicken and garlic until the chicken is no longer pink in the center, 5 to 8 minutes. Pour the wine and diced tomatoes with their juice into the skillet, and bring to a boil over high heat while scraping any browned bits of food off of the bottom of the pan with a wooden spoon.
Stir in the shell pasta, and return to a boil. Cook uncovered, stirring occasionally, until the shells have cooked through, but are still firm to the bite, about 10 minutes. Spread the spinach over the top of the pasta, cover, and simmer until the spinach leaves are cooked, about 5 minutes. Sprinkle the mozzarella cheese evenly over the skillet, and simmer until the cheese has melted and the pasta is bubbling, about 5 minutes.
