Just for clarification, this is specifically the web chat, and not IRC (such as what Chatty uses).
It came to my attention when we had some commands via Nightbot that contained emojis (such as those supported by the Symbola font) are silently removed by the web chat. They seem to show up in Chatty (which uses IRC as mentioned earlier), though. I asked a few others in chat, and they seem to have the same issue (chat was on-stream as well, and their message didn't show up for either me (Google Chrome) or the streamer (Mozilla Firefox)). And just to clarify, no, Nightbot is not in my ignore list. This happened with any user that posted a message containing emojis.

Here is an album that shows it: https://imgur.com/a/wghHY

Anyone else able to test this and verify it's not only a few of us with this issue?