A novel maize variety designated PH134R and seed, plants and plant parts thereof. Methods for producing a maize plant that comprise crossing maize variety PH134R with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into PH134R 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 PH134R or a locus conversion of PH134R with another maize variety.