Misalignment is common in hydrodynamic journal bearings and the causes of it can be diversified, making the lubrication performance exhibits stochasticity. Lubricant viscosity often heavily depends on temperature, which may vary during service and result in unexpected deviations. This article analyzes the stochastic lubrications of a cylindrical hydrodynamic journal bearing with misalignment under uncertainties. The stochastic Reynolds equation governing the misaligned journal bearing is discretized by the polynomial chaos expansion (PCE), an efficient uncertainty tracking tool, and then solved by the finite difference method to obtain sampled lubrication. The crude Monte Carlo simulation is used to verify the performance of the PCE frame. Various critical lubrication performance parameters are studied comprehensively by the ensemble mean, standard deviation, probability density function, and cumulative distribution function. Insightful inspections are provided on the stochastic results, and it is found that the misalignment and different stochastic parameters may cause significant effects on the lubrication performance. The new findings in the present study will guide the robust design and analysis of general hydrodynamic journal bearings.