The speed and stability of magnetic chiral motion are numerically investigated in a chain of asymmetric thin nanodots. The chirality of the magnetization rotation in an asymmetric nanodot plays a significant role in the velocity at low critical field, and there exists a stable operating magnetic field at the intermediate level, irrespective of the arrangement of asymmetric nanodots. Additionally, with induced in-plane anisotropy, we find that the chiral motion yields more stability with a lower critical field at room temperature. We ascribe the shift of the energy barrier as a major contribution to the thermal stability, high speed, and low critical field of chiral motion.