Abstract: A method for producing an olefin product, including the steps of converting a hydrocarbon feedstock to an unsaturated hydrocarbon stream through a steam cracking process in an olefins production plant; combusting hydrogen to provide at least some of the heating duty to the steam cracking process, wherein the hydrogen has a carbon intensity less than about 1.0 kg CO2e/kg H2, wherein the hydrogen is produced using a hydrogen production process; providing at least some of the required energy for the hydrogen production process from a biomass power plant; and processing the unsaturated hydrocarbon stream to recover the olefin product. The olefin product may comprise ethylene having a well-to-gate carbon intensity less than about 0.6 kg CO2e/kg C2H4, or may comprise propylene having a well-to-gate carbon intensity less than about 0.6 kg CO2e/kg C3H6.