A novel inbred maize variety designated PHHCF and seed, plants and plant parts thereof. Methods for producing a maize plant that comprise crossing inbred maize variety PHHCF with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into PHHCF through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby. Hybrid maize seed, plant or plant part produced by crossing the inbred variety PHHCF or a trait conversion of PHHCF with another maize variety. Inbred maize varieties derived from inbred maize variety PHHCF, methods for producing other inbred maize varieties derived from inbred maize variety PHHCF and the inbred maize varieties and their parts derived by the use of those methods.