The need to consider the uncertainty associated with the data used to compute characterization factors has been recognized as a requirement to fully address uncertainty in a life cycle assessment study. However, most of these studies focus on the uncertainty associated with data collected in the Inventory Analysis step, leaving the uncertainty in the parameters used in the Impact Assessment step without analysis. This study addresses this gap and presents a methodology for analyzing the uncertainty related to the characterization factors. This methodology departs from the traditionally deterministic life cycle assessment and explores Monte Carlo simulation to develop a stochastic life cycle assessment. The proposed methodology is applied to the comparison of two pulp bleaching techniques, Elemental Chlorine Free and Total Chlorine Free, to demonstrate how this methodology can be used in a decision-making process. The analysis of the stochastic results indicate that switching from Elemental Chlorine Free to Total Chlorine Free is not the most effective strategy when trying to decrease the overall environmental impact associated with the production of bleached pulp since the two techniques have significantly equal single scores. The proposed methodology and its application to a case study showed the importance of integrating uncertainty analysis into life cycle assessment studies. This integration would be more straightforward if impact assessment methods provided uncertainty distributions for the characterization factors used.