After making Reversible Bucket Hat: Brown Vintage Floral and White Polka Dot Red, I made this purple one with a reversible lime-green-white-mini-polka-dot side! This time I added a chin strap using bias tape and sewed it in when attaching the final hat piece. It stays on much better with wind and looks cute with the strap on the "outside" when reversed as well (not pictured because E says it's "purple's turn" to be on the outside, not "green dots' turn.").
Tutorial and Pattern: Oliver + S Reversible Bucket Hat Free Sewing Pattern