  There is currently a strong interest in the collective behavior of chiral
active particles that can propel and rotate themselves. In the presence of
alignment interactions for many chiral particles, chiral self-propulsion can
induce vortex patterns in the velocity fields. However, these emerging patterns
are non-permanent, and do not induce global vorticity. Here we combine
theoretical arguments and computer simulations to predict a so-far unknown
class of collective behavior. We show that, for chiral active particles,
vortices with significant dynamical coherence emerge spontaneously. They
originate from the interplay between attraction interactions and chirality in
the absence of alignment interactions. Depending on parameters, the vortices
can either feature a constant vorticity or a vorticity that oscillates
periodically in time, resulting in self-reverting vortices. Our results may
guide future experiments to realize customized collective phenomena such as
spontaneously rotating gears and patterns with a self-reverting order.
