Learn Spanish (Latin America): Anoche chateé con mi prima.

The infinitive (dictionary form) of the verb is chatear (to chat). To form the "I" (or yo) form in the preterite past tense for regular -ar verbs, you drop the -ar and add -é. Since the stem of this verb is chate-, adding the ending makes it chateé.

How do I pronounce the double 'e' in chateé?

You pronounce both 'e' sounds, separating them slightly. The accent mark means you put the strong vocal stress on that very last letter: cha-te-EH.

Does chatear mean chatting face-to-face or online?

It is almost exclusively used for chatting online or texting (like on WhatsApp or social media). It comes directly from the English word "chat". If you chatted with your cousin face-to-face, you would use a verb like platicar, hablar, or conversar.

Why don't we need to say yo chateé?

In Spanish, the ending of the verb usually tells you who is doing the action. The -é ending on regular -ar verbs in the preterite tense is only ever used for "I" (yo). Because the verb ending makes it perfectly clear who you mean, you can safely drop the yo.