In this work we propose a bi-criterion, multi-period, stochastic mixed-integer linear programming model that address the optimal design and planning of hydrocarbon biorefinery supply chains under supply and demand uncertainties. The model accounts for diverse conversion technologies, feedstock seasonality and fluctuation, geographical diversity, biomass degradation, demand variation, government incentives and risk management. The objective is simultaneous minimization of the expected annualized cost and the financial risk. The financial risk is measured by conditional value-at-risk. The model simultaneously determines the optimal network design, technology selection, capital investment, production planning, and logistics management decisions. Multi-cut L-shaped decomposition approach is implemented to circumvent the computational burden of solving large scale problems. The capabilities of the proposed modeling framework and solution algorithm are illustrated through the optimal design of the hydrocarbon biorefinery supply chain in the State of Illinois.