Release an addon module that allows integration between ontime and purechat. Linking customers by email address possibly.
Or once a chat session has ended offer the oeprator a way to "push" that chat transcript into OnTime for a specific Customer/Feature/Defect/Incident.
PureChat could be used by customers for product support, we already have customer data in OnTime. Maintaining chat logs from PureChat in Ontime would be a great way to keep all customer data & communications in one place.