The Peierls stress is defined as the minimum resolved shear stress to move a dislocation at absolute zero. It is an important measure of dislocation mobility, a property that controls the strength and ductility of crystals. The Peierls stress has not been well explored in multi-principal element alloys (MPEAs) and would be a useful quantity in predicting mechanical behavior. MPEAs are novel alloys that consist of three or more elements added in near-equiatomic amounts, in contrast to conventional alloys, which are comprised of a single base element with minor alloying elements. The different elements and atomic ratios in MPEAs can lead to properties that are superior to those of conventional alloys. In this study, we investigated the ternary MPEA NbTiZr, a known refractory alloy with potential for high-temperature and aerospace applications. Atomistic simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) were used to calculate the generalized stacking fault energy (GSFE) and Peierls stress of edge, screw, and mixed dislocations on each slip plane of the <111>{110}, <111>{112}, and <111>{123} slip systems. Our results have shown that the various Peierls stresses of NbTiZr are considerably higher than that of pure Nb. This shows that NbTiZr is likely stronger than pure Nb and thus can be a more durable alternative to Nb in current refractory and aerospace applications.