More natural noun for someone who you chat with

Most people I know say chat buddy, internet friend, or online friend like @FumbleFingers and @Kristina Lopez said. You might say penpal. Although it generally means someone you write letters to (and perhaps never meet), I think it is appropriate for a friend you only know online and to whom you write. The following sentences sound natural:

1. I was talking to an online friend the other day.
2. I have a Skype meeting with a chat buddy later.
3. I'm chatting with a buddy.
4. She was my internet friend for years before we ever met in person.
5. I was chatting with my penpal all day yesterday.

Note: in example 3, if you use the word chat (even as a verb) in a sentence, you don't have to say chat buddy, just buddy will work. Buddy already has an "online" connotation, especially used in that context.

The more I think about it, the more I like penpal.

I hope that helps!

FumbleFingers' chat buddy is a good choice but you might also consider online friend.