Simply replace the unfilled areas such as "" and "[date]" with your information.
Dear [name of manager or supervisor],
I would like to request a new seat assignment. I am not comfortable in my current seat assignment due to being located so near [another employee]. This employee and I do not get along and are unable to sit so near each other any longer without resulting tension. I feel that it would be better for both of us, and for our productivity, if one of us was to move to a new location. I understand that this may not seem professional, but I feel that the situation would become very unprofessional if the seating assignments remain the same.
Thank you for considering this request.