It may not always be possible to associate a chat customer with an existing contact record. In this case, you may wish to create a new contact record for the customer seeking support. You can do this directly from the Live Assist widget by clicking on the "+" icon next to the customer's avatar circle.
This will launch the "New Contact" form in the main panel of the application. Complete the form, using information supplied by the customer, and then click the "Save" icon at the lower right.
Note: The Contact card is only available to Agents with the Customer Service Representative or CSR Manager roles assigned.
As of Live Assist for Microsoft Dynamics 365, version 3.6.0 (April 2018 Release), it's possible to use the Automatic Association Tool (Creating New Entities Auto Associated with the Chat Activity) to create contacts.