I don't think there are any 3 that are exactly what you ask about ("chat-on-blockchain thing").
However, from my understanding of Telegram's ICO and "leaked" roadmap, they appear to be doing a decentralized chat the may leverage their own blockchain for some features (identity, tokens etc.).
I think Status.im is another example, but it's currently early access I believe.
My own product, stealthy.im could be another example. The web product is in production. It builds upon blockstack, storing identity and storage pointers in the blockchain.
So that's 3. I could probably list a few more, but again they wouldn't strictly satisfy your precise criteria in one or major ways. I think @jerf's response is really good--for us the "why" of blockchain is in identity and providing a verifiable decentralized storage network through blockstack. The underlying bitcoin blockchain wouldn't be suitable for message storage or sdp handshaking due to latency as another person pointed out.
Thank you for providing an example. It's not a "bunch" but still. Could you explain why did you use word "regrettably", is it a bad thing these projects exists?
I think @detaro says 'regrettably' because of the distaste many have about ICOs and the hype related to them. However, I too would like to hear from @detaro on this.
Pretty much, yeah: pushing actual messaging over a blockchain is just horribly inefficient and I don't see it being a workable idea, so it seems dishonest to me to widely promote it and collect money for it.
Other related things are fine: e.g. mapping public keys to human-readable identifiers like a nickname is a good match to what a blockchain is good at, I get why people like the idea of cryptocoin-payments in a messenger platform, ... Still leaves the general concern of "does this really need it's own coin with an ICO and hype", but at least the ideas make some sense there.