Preheat oven to 350 degrees. Place chicken breasts in 9-by-13-inch glass baking dish. Pour dressing over chicken and bake for 25-30 minutes. Remove from oven and cool.
Cut a slit in middle of chicken breast with sharp knife. Do not cut all the way through. Cut a little pocket on either side of slit, again, making sure not to cut all the way through.
Prepare potatoes according to package directions. Mix in crab. Salt and pepper to taste. Distribute potato mixture evenly among chicken pockets. Sprinkle with cheese. Place in a non-greased baking dish. Bake for 10-15 minutes, or until cheese has completely melted. Remove from oven and garnish with basil. Serve immediately.