The cycle service level (CSL) is frequently used by inventory managers as a metric to measure service quality and set the inventory policy. As retailing enterprises are adopting more and more innovations to integrate their physical and online stores to provide consumers a seamless shopping experience, it raises an essential question regarding omnichannel retailing under CSL requirements. To investigate this question, we propose an omnichannel inventory-pricing newsvendor model, price-based stochastic demand, and CSL-based order quantity to maximize the retailer's profit. It is a chance-constrained optimization problem with the decision variables are all the channels' prices and order quantities. There are many difficulties in solving the maximization problem since no such an analytical verification for the joint concavity of the objective function in all decision variables exists. However, given the equality constraints on CSL, the objective function can be transformed into an equivalent version with decision variables are only the retailing prices. By a novel approach, we prove that the transformed objective function is jointly concave in its variables. Thus, there exists a unique solution to optimization problem under equality constraints.