Dear ...
I have just recently __(applied for a new job-position/been appointed as/etc)__ with __(name of organization)__ and I have been asked to provide them with __(character/reference)__ letter of myself. That is the reason I am writing to you today. I immediately thought of you when I was asked to provide this.
You are a highly respected individual, __(Name)__ and I would be so appreciative if you would be willing to write a __(letter of reference/character reference letter)__ on my behalf. This position will require that I __(briefly describe what is expected of you)__. In keeping with that, the points made in the reference letter should touch on these areas.
I have been looking forward to an opportunity like this for quite some time now and I am very enthusiastic about it. I thank you in advance for taking the time to be of assistance to me in this matter. If there is any additional information that you require, please feel free to contact me at __(phone #)__. Once again, I thank you for all you help, __(name)__.
Sincerely,