Good idea

~5:00 PM Eastern Time is probably the easiest for most time zones, including Europe. I will send the bot in sometime around then as well, and will probably leave it there through the evening.
Keep in mind that daylight savings time should be considered, for those who don't go by it. Check my profile to see to what I'm referring as 5:00 ("user's local time" is the time zone).
Also, for everyone, if you come to the chat around 5:00 and no one is there, idle a little bit. More are very likely to come, but if people leave at the moment they sign in, the chat will remain empty regardless of how many came.