Originally Posted by WillCAD

I think OP was referring to travel chopsticks, which break down to a small size when not in use. Like these from Amazon:
Rosewood Foldable Wood Chopsticks with Carrying Pouch

I've had travel chopsticks in the past, both stainless and plastic, and have yet to find a pair I like. The ends all tend to be too blunt, and I can't get a good grip on food with them. If I could find a set with pointier ends, I'd probably buy a dozen sets.

EDITED TO ADD: I would imagine that wooden or bamboo chopsticks, especially those that break down for storage, wouldn't be prohibited items, since they're basically the same as pencils or pens with no lead or ink. But I searched the TSA What Can I Bring? page for 'chopsticks', 'chop sticks', and 'chopstix' and got no returns on any of them, so it's not an explicitly allowed or prohibited item. What that means, alas, is that screeners have probably never been trained whether chopsticks are allowed or not, so it will be up to the infamous "individual discretion" whether your travel set is allowed. I'd recommend sticking with an inexpensive set that won't set you back much if it's compulsorily voluntarily surrendered. Which, unfortunately, is good advice for just about anything you carry with you when traveling by air, since both confiscation and theft are real possibilities.