As part of our comprehensive long-term multi-waveband monitoring of 34 blazars, we followed the activity in the jet of the blazar PKS 1510-089 during major outbursts during the first half of 2009. The most revealing event was a two-month long outburst that featured a number of gamma-ray flares. During the outburst, the position angle of optical linear polarization rotated by about 720 degrees, which implies that a single emission feature was responsible for all of the flares during the outburst. At the end of the rotation, a new superluminal knot (~ 22c) passed through the "core" seen on 43 GHz VLBA images at essentially the same time as an extremely sharp, high-amplitude gamma-ray and optical flare occurred. We associate the entire multi-flare outburst with this knot. The ratio of gamma-ray to synchrotron integrated flux indicates that some of the gamma-ray flares resulted from inverse Compton scattering of seed photons outside the ultra-fast spine of the jet. Because many of the flares occurred over time scales of days or even hours, there must be a number of sources of IR-optical-UV seed photons -- probably synchrotron emission -- surrounding the spine, perhaps in a slower sheath of the jet.