  We have calculated a complete set of primary fission fragment mass yields,
$Y(A)$, for heavy nuclei across the chart of nuclides, including those of
particular relevance to the rapid neutron capture process ($r$ process) of
nucleosynthesis. We assume that the nuclear shape dynamics are strongly damped
which allows for a description of the fission process via Brownian shape motion
across nuclear potential-energy surfaces. The macroscopic energy of the
potential was obtained with the Finite-Range Liquid-Drop Model (FRLDM), while
the microscopic terms were extracted from the single-particle level spectra in
the fissioning system by the Strutinsky procedure for the shell energies and
the BCS treatment for the pairing energies. For each nucleus considered, the
fission fragment mass yield, $Y(A)$, is obtained from 50,000 -- 500,000 random
walks on the appropriate potential-energy surface. The full mass and charge
yield, $Y(Z,A)$, is then calculated by invoking the Wahl systematics. With this
method, we have calculated a comprehensive set of fission-fragment yields from
over 3,800 nuclides bounded by $80\leq Z \leq 130$ and $A\leq330$; these yields
are provided as an ASCII formatted database in the supplemental material. We
compare our yields to known data and discuss general trends that emerge in
low-energy fission yields across the chart of nuclides.
