This work addresses the integrated optimization of upstream and downstream processing strategies of a monoclonal antibody (mAb) under uncertainty. In the upstream processing (USP), the bioreactor sizing strategies are optimized, while in the downstream processing (DSP), the chromatography sequencing and column sizing strategies, including the resin at each chromatography step, the number of columns, the column diameter and bed height, and the number of cycles per batch, are determined. Meanwhile, the product's purity requirement is considered. Under the uncertainties of both upstream titer and chromatography resin yields, a stochastic mixed integer linear programming (MILP) model is developed, using chance constrained programming (CCP) techniques, to minimize the total cost of goods (COG). The model is applied to an industrially relevant example and the impact of different USP:DSP ratios is studied. The computational results of the stochastic optimization model illustrate its advantage over the deterministic model. Also, the benefit of the integrated optimization of both USP and DSP is demonstrated. The sensitivity analysis of both the confidence level used in the CCP model and the initial impurity level is investigated as well.