Place chicken breasts in a plastic bag or between two sheets of heavy plastic. Pound the chicken until it is 1/4 inch thick. Preheat oven to 375 degrees.

In a skillet, heat olive oil over medium heat. Add onions and sauté a few minutes, until soft. Add in garlic and cranberries, and sauté an additional 2 minutes. Add in spinach, balsamic vinegar, thyme, salt and pepper and cook until spinach is wilted.

Lay chicken breasts onto a clean work surface and spoon 1/4 of the spinach mixture onto each chicken breasts. Layer on a few pieces of sliced Parmesan cheese. Roll the chicken breasts around the spinach stuffing and secure with a few pieces of twine or with toothpicks. Season outside of chicken breasts with thyme, salt and pepper.

Warm the same skillet over medium heat, adding a little olive oil, if necessary. Add stuffed chicken breasts to the pan and brown on all sides. Transfer to a baking sheet and bake in preheated oven for 30 - 35 minutes, or until chicken is no longer pink and internal temp has reached 165 degrees.