Do you know why you got downvoted?
1) Because your question can't be answered. Actually it can be: it all depends on you, on how and what you code. Of course a chat application using asp.net and sql server can be made. There are many successfull implementations out there. If you want to know you can do it? Well, if you ask such questions... I have my doubts...
2) And we got to the second cause: what is stopping you to loog for one of them, consult the code and learn from it? Lazyness? Or is goole not available at your place? Just one of them right here, at CP:
ASP/SQL Server Based Chat program[
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