Why do I have a reappearing "trash" folder and "hostsindex" file on my desktop (Mac OS X.6.6)

I delete them, and they reappear about a minute later. I have exhausted Apple, Google, et al to no avail.

The trash folder always says “no items” and the hostsindex file has no extension and contains no data. “Get Info” says nothing significant of either of these files.

I believe these first started appearing after I upgraded to 10.6.6, but I’m not positive they’re related.

Any ideas?