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You can host a video stream (but make it low-def; 1000 people x 1MBPS = 1GBPS)

Alternatively use a centralized service (YouTube, Twitch).

Or, there's also the P2P Jami (but this requires the participants to install something):

but a lot of embarrassing noise if it would work just fine in 3 hours. tough call. I suggest using an IRC channel for the event instead.

It's even more embarrassing if it ends up not working. Better safe than sorry.

wooooooooooooooooooooooosh

Please what? Who is your audience that more then 20% of them could reliably run an IRC client and join the right server?

I believe that was a joke.

What's the quick alternative out of interest? And is it free?

I'd say Jitsi, though I'm not sure how it handles 1000 people.

It doesn't.

It can. If the jitsi has proper videobridges setup it can.