Let’s assume that we have the following piece of code:
Session["username"] = GetUserByCredential(username, password);
It is possible to view that session in Google Chrome ?
I tried to see in Resources tab but no success.

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The Session you are talking about is a server side datastructure inside the webserver / web application.
You cannot access that directly from the client.
You will have to send the content of the current session to the client to view it:
And a view similar to this: