Classic maple syrup urine disease (MSUD) results from biallelic mutations in genes that encode the branched-chain α-ketoacid dehydrogenase E1α (BCKDHA), E1β (BCKDHB), or dihydrolipoamide branched-chain transacylase (DBT) subunits, which interact to form the mitochondrial BCKDH complex that decarboxylates ketoacid derivatives of leucine, isoleucine, and valine. MSUD is an inborn error of metabolism characterized by recurrent life-threatening neurologic crises and progressive brain injury that can only be managed with an exacting prescription diet or allogeneic liver transplant. To develop a gene replacement therapy for MSUD, we designed a dual-function recombinant adeno-associated virus serotype 9 (rAAV9) vector to deliver codon-optimized BCKDHA and BCKDHB (rAAV9.hA-BiP-hB) to the liver, muscle, heart, and brain. rAAV9.hA-BiP-hB restored coexpression of BCKDHA and BCKDHB as well as BCKDH holoenzyme activity in BCKDHA^−/− HEK293T cells and did not perturb physiologic branched-chain amino acid homeostasis in wild-type mice at a systemic dose of 2.7 × 10¹⁴ vector genomes per kilogram. In two models of severe MSUD (Bckdha^−/− and Bckdhb^−/− mice) and a newborn calf homozygous for BCKDHA c.248C>T, one postnatal injection prevented perinatal death, normalized growth, restored coordinated expression of BCKDHA and BCKDHB in the skeletal muscle, liver, heart, and brain, and stabilized MSUD biomarkers in the face of high protein ingestion. In summary, we developed a one-time BCKDHA-BCKDHB systemic dual-gene replacement strategy that holds promise as a therapeutic alternative to prescription diet and liver transplant for treatment of MSUD types 1A and 1B, the two most common forms of MSUD in humans.