Ash here from the Shopify team. Welcome to the Shopify Community!
It sounds like you're experiencing an issue with a domain transfer, and I'm happy to help out right here on our forums! In order to give you the most accurate direction, do you mind elaborating on the situation for me please? Are you trying to connect a third-party domain to Shopify for use on your website, or are you trying to transfer it over to Shopify for hosting as well? We have some documentation on both cases in our Help Center you can reference as well.
For the future, in order to contact our live chat support, start by heading to the contact page on our Help Center. From there, you can either log in to your account or choose continue without logging in. Either option will allow you to proceed with the same steps. On the next page, you'll need to search for a topic, which will display a number of resources related to that topic. If none of those resources solve your issue, or if you simply prefer to reach out to our team directly, scroll to the bottom of those options and there should be a button to proceed to our available support options.
Let me know what your plan is regarding your domain and I'll be happy to provide some more specific direction if needed.