Q: does apple have live chat

Hi,

Not here in the communities but there are other ways to contact Apple for support >  Contact - Official Apple Support

As Carolyn suggests, Apple MAY offer chat for some support issues

If you are "shopping" check near the bottom of any product page

Depending on your issue, they may offer chat as one of the options available (along with email, online support/repair request, etc); however, you need to go through the "questionnaire" starting with the article you referenced. It depends on your issue.

Since you asked about service/support, the option offered when you are shopping will not be helpful - they do not offer product support.