Sellmytimesharenow.com, based in Exeter, New Hampshire is a legitimate business in the sense that it is actual. However there are many, many complaints about this company.
The Better Business has been aware of this company since 2004 and has addressed the complaint history with the company. You should read the entire BBB review here and the complaint history and determine whether this company is for you, since they do not guarantee a time frame for the selling of your timeshare.
But is it a legitimate company? Yes.
Just checking in to see if you need more help or any clarification of my answer. If so, please reply here on this question thread.