Add live chat support on member page only

I want to add livechat to my website (Preferably a Shopify website) on my member page only. My probleme is i already add the live chat on the page that are accesible to member only but the livechat box is related to a url (i thinks it's a Iframe). So a member will be able to open the chat box in a new tab(right click on the chat box) extract the url and give acess to the live chat to someone whos not a member.If a member share my website member page URL it wont work but if they take the livechat box URL provide from a livechat software compagnie it will work.

Does anybody know a way i can do that or a livechat software that i can add to my website that not related to a URL / not sharable?