Ventricular tachycardia (VT) is a life-threatening cardiac arrhythmia for which a common treatment pathway is electroanatomical mapping and ablation. Recent advances in both noninvasive ablation techniques and computational modeling have motivated the development of patient-specific computational models of VT. Such models are parameterized by a wide range of inputs, each of which is associated with an often unknown amount of error and uncertainty. Uncertainty quantification (UQ) is a technique to assess how variability in a the inputs to a model affects its outputs. UQ has seen increased attention in computational cardiology as an avenue to further improve, understand, and develop patient-specific models. In this study we applied polynomial chaos based UQ to explore the effect of varying the tissue conductivity of fibrotic border zones in a patient-specific model on the resulting VT simulation. We found that over a range of inputs, the model was most sensitive to fibrotic sheet direction, and uncertainty in fibrotic conductivity resulted in substantial variability in the VT reentry duration and cycle length. Overall this study paves the way for future UQ applications to improve and understand VT models.