Hi Christian,
There is a Chats Per Hour built-in report that creates simple chat counts on a per-day, per-hour basis. So you can see how many chats you're getting on Mondays at 5pm, Tuesdays at 8pm, etc, over a date range and with the usual LH3 report filters (queues, answered/not-answered, minimum duration). This can be downloaded to a CSV file so you could look at groups of hours (Mondays from 8am-5pm, Mondays from 5pm - 11pm) with some spreadsheet work.
If it turns out this isn't quite getting at what you need (especially for your collaborative service), definitely let us know at LibraryH3lp support. We generate custom reports quite often, especially when the built-in stuff won't do the trick.