This is not possible currently - chat bots are, by design, available 24/7. I would like to see this change too, however, as when a chat bot is used to control the handoff to a human operator, it gets messy outside of those operaters' hours or when they forget to set their away message.
I recommend you search the ideas forum for an existing submission like this or post your idea over there so that we can vote on it.
Hope this helps.
I strongly agree with the idea and already upvoted it.
I think the easiest way would be to have at least the possibility to set the timing for the targeted messages.
In this way we could:
Would this idea fit everyone's needs?
In this case I don't think it should be too difficult for HubSpot to release this feature, we can already target the pages where we want the targeted message to be shown, so only a "timing" rule should be added...