The uncertainty in infusion durations and non-homogeneous care level needs of patients are the critical factors that lead to difficulties in chemotherapy scheduling. We study the problem of scheduling patient appointments and assigning patients to nurses under uncertainty in infusion durations for a given day. We consider instantaneous nurse workload, represented in terms of total patient acuity levels, and chair availability while scheduling patients. We formulate a two-stage stochastic mixed-integer programming model with the objective of minimizing expected weighted sum of excess patient acuity, waiting time and nurse overtime. We propose a scenario bundling-based decomposition algorithm to find near-optimal schedules. We use data of a major university hospital to generate managerial insights related to the impact of acuity consideration, and number of nurses and chairs on the performance measures. We compare the algorithm with several relevant scheduling heuristics and assess the value of stochastic solution.