  We investigate the viscosities of the quark-gluon plasma in strong magnetic
fields within the leading-log and lowest Landau level (LLL) approximations. We
first show that the bulk viscosity in the direction parallel to the magnetic
field is the only component that has a contribution from the quarks occupying
the LLL. We then compute the bulk viscosity from the Kubo formula and find an
intriguing quark-mass dependence as a consequence of a competition between the
suppression of the bulk viscosity by conformal symmetry and an enhancement of
the mean-free path by chirality conservation, which governs the behavior in the
massless limit. The quark contribution to the viscosity along the magnetic
field becomes larger than the one in the absence of a magnetic field. We also
briefly estimate the other transport coefficients by considering the
contribution of gluons. We show that the shear viscosities are suppressed
compared to their values in the absence of a magnetic field.
