Motivated by the three-dimensional serpentine channel (Liu et al. in J Microelectromech Syst 9:190197, 2000), we introduce a chaotic serpentine mixer (CSM) and demonstrate a systematic way of utilizing a mapping method to find out an optimal set of design variables for the CSM. One periodic unit of the mixer has been designed to create two streamlines portraits crossing each other. As a preliminary study, flow characteristics and mixing in the original serpentine channel has been reinvestigated. The working principle of the CSM is demonstrated via a particle-tracking method. From the design principle and the flow characteristics of the CSM, we choose three key design variables with an influence on mixing. Then, simulations for all possible combinations of the variables are carried out. At proper combinations of the variables, almost global chaotic mixing is observed in the Stokes flow regime. The design windows obtained can be used to determine an optimal set of the variables to fit with a specific application.