A novel maize variety designated PHR1R and seed, plants and plant parts thereof. Methods for producing a maize plant that comprise crossing maize variety PHR1R with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into PHR1R 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 variety PHR1R or a trait conversion of PHR1R with another maize variety. Inbred maize varieties derived from maize variety PHR1R, methods for producing other inbred maize varieties derived from maize variety PHR1R and the inbred maize varieties and their parts derived by the use of those methods.