  We consider the orbits of particles with spin in the Schwarzschild spacetime.
Using the Papapetrou-Dixon equations of motion for spinning particles, we solve
for the orbits and focus on those that exhibit chaos using both Poincar\'e maps
and Lyapunov exponents. In particular, we develop a method for comparing the
Lyapunov exponents of chaotic orbits. We find chaotic orbits for smaller spin
values than previously thought and with spins that could be realized
astrophysically.
