A pet tribble (presumably desexed) was once known to have existed in the kindergarten of the USS Enterprise-D, it was disposed of by Lieutenant Worf’s son, Alexander, during a rather bloody show-and-tell session involving his father’s bat’leth. Worf is believed to have skinned the creature and presented the fur as a toupee in a sign of respect to his captain. Captain Picard politely declined the gift, but his debonair first officer Commander Riker cheerfully agreed to wear it on the end of his chin.
This tradition among Starfleet officers of wearing a tribble has apparently carried through to the present day. A holoimage of Captain Kathryn Janeway, taken on the eve of Voyager’s ill-fated maiden journey, shows her with what appears to be an enormous red tribble on top of her head.