DD2 used to like to flick the chain around and put it in her mouth, but she would also try and suck on the trolly handle too. If I took her shopping I would be constantly moving my hands along the handle so she'd suck on my hand instead of the trolley and I'd keep the chain out of her mouth.

Just one of those things you have to keep an eye on if you have a toddler in the trolley, not a safety hazard.