Place each chicken breast between 2 sheets of heavy-duty plastic wrap; pound to 1/4" thickness using a meat mallet or rolling pin. Sprinkle chicken with salt and pepper.
Spread 2 tablespoons Crabmeat Dip over each chicken breast. Divide spinach evenly over dip; roll up chicken, jelly-roll fashion. Wrap each roll with 1 slice prosciutto; secure with a wooden pick.
Heat oil in an ovenproof skillet over medium-high heat. Add chicken, and cook 3 to 4 minutes on each side or until prosciutto is lightly browned and crispy. Place skillet in oven, and bake at 350° for 25 minutes or until chicken is done. Remove wooden picks before serving.
Note: Make Crabmeat Dip no more than 1 day ahead of preparing Crabmeat-Stuffed Chicken Breasts.