The space motions of chromospherically active late-type dwarfs (solar-type stars, K and M dwarfs, and BY Draconis binaries) are illustrated and discussed. Except for a small number of deviant stars, all the active single stars have the kinematics of young stars (age about 0.5 Gyr). The most egregious exception is HD 152391, which appears to be a single star with a high level of chromospheric activity but with the kinematics of the old disk population, for reasons unknown. The BY Dra binaries, with a few exceptions, also have the kinematics of youth, being characterized by an age of about 1-2 Gyr. This lack of old BY Dra binaries seems puzzling, since a binary should be able to draw on orbital angular momentum to maintain rapid rotation well into old age, but this dearth is suggested to be due to the very rapid loss of angular momentum that a double star can maintain until essentially all the angular momentum is lost and the stars coalesce. No strong kinematic coherence is seen among the active single stars, indicating that these stars were born in many different nurseries and have come to the solar neighborhood through random processes. 70 refs.