  We show that the Big Bang Observer (BBO), a proposed space-based
gravitational-wave (GW) detector, would provide ultra-precise measurements of
cosmological parameters. By detecting ~300,000 compact-star binaries, and
utilizing them as standard sirens, BBO would determine the Hubble constant to
0.1%, and the dark energy parameters w_0 and w_a to ~0.01 and 0.1,resp. BBO's
dark-energy figure-of-merit would be approximately an order of magnitude better
than all other proposed dark energy missions. To date, BBO has been designed
with the primary goal of searching for gravitational waves from inflation. To
observe this inflationary background, BBO would first have to detect and
subtract out ~300,000 merging compact-star binaries, out to z~5. It is
precisely this foreground which would enable high-precision cosmology. BBO
would determine the luminosity distance to each binary to ~percent accuracy.
BBO's angular resolution would be sufficient to uniquely identify the host
galaxy for most binaries; a coordinated optical/infrared observing campaign
could obtain the redshifts. Combining the GW-derived distances and EM-derived
redshifts for such a large sample of objects leads to extraordinarily tight
constraints on cosmological parameters. Such ``standard siren'' measurements of
cosmology avoid many of the systematic errors associated with other techniques.
We also show that BBO would be an exceptionally powerful gravitational lensing
mission, and we briefly discuss other astronomical uses of BBO.
