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. BBOs 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. BBOs 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.
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