Yeah, quill stems can be confusing. The two commons sizes for quill stems are 1" and 1-1/8". The first has been used on road bikes for a long time, and older MTBs. The second was used on MTBs shortly before the industry switched over to threadless stems. What you need is called a 1" stem, even though it measures 7/8" (don't ask me why). If your new stem measures 1" outside, then technically it's a 1-1/8" stem.

So when shopping, make sure to look for something marked as a 1" stem. You could either get a quill in that size, or go the with a quill-to-threadless adapter, as others have noted.

See http://sheldonbrown.com/gloss_st-z.html#stem for more info.