I have begun using Google Chrome as a primary browser, but I miss my Evernote extension, which can clip a web page directly to the local Evernote application. Is it possible for me to write an extension in Chrome that can do this?
Editor's note: This old answer may be useful for historical purposes, however, note that NPAPI Plugin support for extensions has long been discontinued. Use native messaging instead.
Yes it is possible, through NPAPI, but your local application should be prepared for external communication. Code running in an NPAPI plugin has the full permissions of the current user and is not sandboxed or shielded from malicious input by Google Chrome in any way.
All this is described here: http://code.google.com/chrome/extensions/npapi.html