Is it possible to run at the same time a couple Windows Store Applications? I have written a chat application (in C#), and want to test it on one PC, but I can't make it work.
Is there any option to do this? Or any ideas how to get around it?
No, Windows Store apps are strictly single instanced, see this post:
http://social.msdn.microsoft.com/Forums/en-US/windowsdeveloperpreviewgeneral/thread/daf6f12f-b54d-4550-a70d-d92e6e06bfdc
Howerer there might be a solution, if you are owner of that app and you have access to source code and project, just build and deploy the app, change the app Name and ID in manifest file and deploy it again - it should be then shown as another app in Start screen. Note I have not tested this, but it worked fine for Windows Phone apps, so I guess it should work on Windows 8 as well?