Learn Spanish (Latin America): Chatearon mucho anoche.

Chatearon is the completed past tense (preterite) form of the regular verb chatear. To say "they [did something]" for regular -ar verbs in the past, you drop the -ar and add the ending -aron.

Where is the word for "they" in this sentence?

In Spanish, the subject pronoun is usually dropped if the verb ending makes it clear. The -aron ending on chatearon tells us the subject is "they" (ellos or ellas) or "you all" (ustedes). You could add the pronoun at the beginning, but it's completely natural to leave it out.

Is chatear just the English word "chat" turned into a Spanish verb?

Yes! It's a modern loanword. However, keep in mind that chatear specifically means to chat online or send text messages. If you want to talk about having a spoken conversation, you would use verbs like hablar (to talk) or platicar (to chat/converse).

Why is it mucho instead of muchos?