For example, could you please provide at least 3 (a bunch) examples which are in production?
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.
just this week I saw https://adamant.im
There was a thing called "my echo" (which appears to have failed/been cancelled).
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.