Download doPDF and install.
Let it to install its driver.
Then it will act as a printer (a virtual printer)
Print your ASHX through doPDF printer.
Then you will have a option to save your file as pdf
@LeonardKonrad - first this is a thread from May 2011. Second, I think you totally missed the original question. Its not that he can't make it a pdf, its that he couldn't open the ashx file on his computer.
I think the .ashx extension has something to do with the ASP.NET framework used by Google Chrome. I don't understand the technical aspects, but it's annoying. Sometimes I actually use Internet Explorer (gasp!) when I'm downloading email attachments to avoid the problem.