Not always required. Commonly used in smaller planes, less so in bigger ones. Similar in Canada.
I'm not absolutely sure of the rules but this seems to be the case:
Parachute not required by FAA. Some STC's or 337's or what have you do require it, e.g. the flip-up in-flight door modifications for typical single piston engine Cessna used for skydiving. Some dropzones may require pilots to wear a chute. There's more of a push to wear one for low tail aircraft (e.g., Caravan), but less so for higher tail aircraft (e.g., Twin Otter, Skyvan, CASA), where there's less chance of a premature parachute opening by a skydiver taking out the tail or catching on the tail and causing control problems.