I got a chemical peel on a targeted area. A month later, I have a pink spot on my forehead. Will this fade?

When treating any area of the face or body with any procedure, it is always recommended for best results to treat the entire area. It will give a more uniformed result. By spot treating, there can be an uneven skin texture and tone. 

Your red spot should fade in time.  Return to your provider for assistance with management.  You don't mention what was being treated with the targeted chemical peel but it may require ongoing treatment and follow-up.  The acid causes a controlled damage to the skin and new cells regenerate as the healing process occurs.  A cell cycle is about 120 days.  Hope this helps and good luck.