No, not at all. Chrome is my (and many other users) preferred browser. I just used Chrome to authenticate with Facebook on your site. My account was created and I was logged in automatically, as expected.
I'd suggest checking any add-ons you have for Chrome that may be blocking social networks (usually for privacy purposes) or try from a different computer entirely to see if you have the same behavior.
I hope that helps you narrow things down, but if you run into issues, please let me know.
Thanks,
Alex