Inspired by recent innovations in the retail industry, we study an on-demand personal shopper service that lets customers shop online for products from brick and mortar stores. A fleet of personal shoppers fulfills customer orders, performing both shopping at the stores and delivery to the customers. The operation of such a service requires to dynamically offer service to incoming shopping and delivery requests, coordinate a fleet of shoppers, schedule shopping operations at stores, and execute deliveries to customers on time. This paper studies this new problem and proposes three different order-consolidation strategies for service operators. Our numerical results show that order consolidation, particularly shopping consolidation, can significantly increase the number of served orders by better using the available shopper capacity. We observe that splitting orders can further enhance the performance of the system. The results also suggest that personal shopper services increase time utilization and execute shopping activities using significantly less human resources than customers shopping for themselves.