Gossiping is certainly speech. I would have thought it to be protected:
"Four town employees with 46 years of service between them were fired, in part for gossiping and discussing rumors of an improper relationship between the town administrator and another employee that Hooksett residents now agree were not true.
The administrator complained, and after an investigation the town council fired the women, finding, 'Gossip, whispering, and an unfriendly environment are causing poor morale and interfering with the efficient performance of town business.' ...
'We discussed it on a lunch break, and then it ended.' 'It kind of sort of was, 'Oh did you hear that too," said Michelle Bonsteel, Piper's fired co-worker."
Source
