Expenditure for energy utilities is significant for most process plants. The identification and implementation of various energy conservation projects are essential in reducing the operating cost and greenhouse gas emissions associated with energy use. Typically, energy conservation projects need capital investments drawn from limited funding sources. Appropriate selection of these projects is important to ensure overall financial and environmental benefits. Varying energy prices, an evolving carbon emissions regulatory regime, changes in product quality, energy efficiency requirements, and unscheduled maintenance of different process equipment/units make the overall financial returns inherently uncertain. In this work, Financial Pinch Analysis is extended to incorporate uncertainties for the appropriate selection of energy conservation projects. Monte Carlo simulations are performed to account for various sources of uncertainty in financial return metrics for the energy conservation projects. A stochastic linear programming problem is formulated to identify appropriate energy conservation projects. The chance constraint programming method is applied to convert the original stochastic linear programming problem into a deterministic Pinch Analysis framework at different reliability levels. The applicability of the proposed method is illustrated through an example.