Is it possible to replace that rotted window sill?

It is possible to replace a rotten window sill, though the process is labor-intensive.  For one, getting the old sill out without damaging your walls, trim and other structural parts is a touchy business.  Creating the replacement sill from scratch is a job for an experienced woodworker or a carpenter.  Pre-made sills do exist, but their application may not be as user-friendly and the aforementioned steps still come into play.  Depending on how rotted the sill actually is, there could be much more work needed than just replacing that sill, since the moisture would have likely penetrated the walls and window frame as well. 

Unless you are completely confident in your ability to perform the work, it is probably wise to leave this job to the pros.  Doable and looks good when finished are two separate things.  Also, don't forget that the sill is a notorious escape route for your home's heating and cooling if the finished job isn't properly sealed. Professionals can better determine the extent of the repairs necessary.  Of course, Calfinder contractors can have that old sill fixed up in a jiffy if you want to save your back.