Dear …
On __(date)__, I was fortunate enough to have been offered the position of __(name of position)__ with __(name of company)__. At that time, however, I was torn between an offer from my previous employer and your organization. The decision was a very difficult one for me and in the end, I decided to take the offer from the company that I was already familiar with, my previous employer.
Having worked there now for __(# weeks/months)__, I have come to realize that this was not the best choice for me after all. It has become very evident that it is not a good fit for me, hence my letter to you today. I am writing to you in hopes that you have kept my resume on file and that there may still be an employment opportunity for me within your organization.
I am asking you to once again consider me for the position of __(type of position)__, with __(name of company)__. I can assure you that, given a chance to prove my abilities, you would not be disappointed with my performance. An opportunity to discuss this further with you would be most welcomed. Please feel free to contact me at __(phone #)__ __(at anytime/in the evenings/etc.)__.
I greatly appreciate your consideration of my request and look forward to hearing from you soon.
Sincerely,