My little boy has a sun hat (which he doesn't much like to wear...) but it doesn't have a chin strap. Whoever designed hats for toddlers without chin straps obviously is NOT a parent. Because this guy does not like to keep his hat on. So I attached a strap.
1. I sewed a tube of fabric.
2. I turned the tube inside-out with a safety pin (you know what I mean, right?) to hide the line of stitches.
3. I put a string of elastic through the tube.
4. I cut a few stitches from each side of the hat's lining to insert the tube and elastic.
5. I sewed it all shut! Not perfect, but I think it'll work for awhile.