Chat seems to be included in the list of filters for export:
(filtersOn=true, filters=[AnnouncementService, AssignmentService, AssessmentEntityProducer, ContentHostingService, CalendarService, ChatEntityProducer, DiscussionService, MailArchiveService, SyllabusService, RWikiObjectService, DiscussionForumService, WebService, LessonBuilderEntityProducer, PollListManager])

While the tool is added to the import site if it doesn’t already exist, any additional chat rooms created in the export site are not imported.

The export file lists the other rooms, but they are not imported:

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