Heat 2 tablespoons olive oil in a large skillet over medium heat. Add chicken; cook until beginning to brown, about 4 minutes. Reduce heat to medium; add onion and garlic. Cook until onions are soft and juice from chicken runs clear, about 4 minutes more. Transfer chicken, onion, and garlic to a plate.

Heat remaining 2 tablespoons olive oil in the skillet over medium-high heat. Add beans and cook until crispy on the outside and creamy on the inside, about 8 minutes. Add cooked chicken, onion, and garlic to the skillet and cook until heated through, about 2 minutes more. Remove from heat.

Stir spinach and Parmesan cheese into the skillet. Season with salt and pepper.