Chase Charge Cards - Watch out for false late fee on first bill

We just received our first bill from our Chase charge card. We acknowledge appropriate charges, except a "late fee" for a bill for our annual fee. We've never received any prior bill from Chase. While we agree to pay the annual fee, we don't feel we should pay the late fee and interest on top of the annual fee (for being late), when they never sent us a prior bill.

We called and found their customer help desk to be rude. It was unclear to us what their customer help desk does.

We suspect Chase has a rip off scheme to charge customers more money, for their airline promo credit cards (UA) by saying they sent an earlier bill for the annual fee, but they don't send this bill.