Since we can assume everyone's on Python 3 by now, the example by @berto in https://stackoverflow.com/a/13354482 can now be considerably shorter:

#!/usr/bin/env python3

from http import server

class MyHTTPRequestHandler(server.SimpleHTTPRequestHandler):
    def end_headers(self):
        self.send_header("Access-Control-Allow-Origin", "*")
        super().end_headers()

server.test(HandlerClass = MyHTTPRequestHandler)

(Note: I was trying to post this as a comment, but you can't have code blocks in comments?)