So, a lot of people have been wondering how not be publicly available to chat by members of their Gplus circles.
Here is how I did it.

a. “Google+ settings” from the top right menu after going to your google plus page.
b. Click “Profile and Privacy” from the menu on your left.
c. In the “Google Profiles” section, click on “edit visibility on profile”. You wil be taken to a view of your profile by external people.
d. Right next to “Send a message” you will see an icon. Click that to make changes. Un-check the “Allow people to send you a message from your profile” and select “only you” (or any other combination that you prefer) in the area below.

Done!