Q:

How to process request with chain of webapp. RequestHandler

GAE webapp allows to map single handler to a route:
application = webapp. WSGIApplication([
                                     ('/login', gae_handlers. UserLogin),
                                     ], debug=True)

Is there any way I can have a chain of request handlers? 
I want to have handler which does authentication before all other handlers run. 

A:

You can do this either with decorators or with WSGI middleware. 
There's a good example of using a decorator in this answer.   Nick Johnson's AEoid project uses the middleware approach.