Janette’s got a great playground hack:
While in the baby swings at the park, my 7 month-old (teething) daughter kept chewing on the edge of the swing. I snapped a bib over the edge and through the leg holes and she happily chewed on her bib while swinging. It moved around a little bit, but it was definitely better than the filthy black rubber. This could work for teething babies in grocery carts, too.
Related: Plenty of teething hacks at Parent Hacks