Cut a deep, horizontal pocket in the side of each chicken breast. Make the pocket as large as you can without piercing the top or bottom of the breast. Place 2 lemon wedges, 1 tablespoon basil, and 1/2 of spinach in pocket of each chicken breast.
Secure pockets with toothpicks, threading along the side to close.
In heavy skillet, heat oil over medium-high. Add stuffed chicken to skillet and cook on each side until golden brown, about 4 minutes per side.
Add vinegar and chicken broth, bring to boil. Lower heat and gently simmer chicken for 4 to 6 minutes until cooked through.
Remove chicken breast to serving plate and cover with foil to keep warm. Continue to cook sauce until it is reduced to thick syrup.
Taste sauce and season with the salt and pepper. Spoon the sauce over chicken and serve.