2) A shortened version of "channel" used to refer to textboards and imageboards.
3) A person that the userbase of imageboards have grown fond of or obsessed over.
As an honorific, chan is a suffix added to the end of one's name as a form of endearment. Though typically used for babies, pets and young girls, the term has been picked up but the English speaking anime community and is used more frequently with admiration as the only common factor.
As a common naming theme for text and imageboards, the term is typically used in a plural state, "chans", and used to refer to numerous boards at once. This term began with 2channel, a Japanese textboard and the world's largest forum, and is often connected to 4chan for being the most popular of the chans in Western internet culture.
On the imageboards, sometimes people post imagery of themselves/another specific person (or things related to themselves/someone else) and it catches the attention of the userbase. These people are called chans due to immense admiration or contempt. This aspect of chan culture has been described as both "a great fondness" and "overly obsessive" due to the userbase's desire to find more and more about the topic individual.
- OMG, Julie-chan is sooo kawaii~
- So, I was scrolling the chans last night and you'll never guess what they heard I liked!
- I desire more pictures of Pear Chan, she is amazingly hot.