The recent discovery by Pan-STARRS1 of 1I/2017 U1 (`Oumuamua), on an unbound and hyperbolic orbit, offers a rare opportunity to explore the planetary formation processes of other stars, and the effect of the interstellar environment on a planetesimal surface. 1I/`Oumuamua's close encounter with the inner Solar System in 2017 October was a unique chance to make observations matching those used to characterize the small-body populations of our own Solar System. We present near-simultaneous g$^\prime$, r$^\prime$, and J photometry and colors of 1I/`Oumuamua from the 8.1-m Frederick C. Gillett Gemini North Telescope, and $gri$ photometry from the 4.2 m William Herschel Telescope. Our g$^\prime$r$^\prime$J observations are directly comparable to those from the high-precision Colours of the Outer Solar System Origins Survey (Col-OSSOS), which offer unique diagnostic information for distinguishing between outer Solar System surfaces. The J-band data also provide the highest signal-to-noise measurements made of 1I/`Oumuamua in the near-infrared. Substantial, correlated near-infrared and optical variability is present, with the same trend in both near-infrared and optical. Our observations are consistent with 1I/`Oumuamua rotating with a double-peaked period of $8.10 \pm 0.42$ hours and being a highly elongated body with an axial ratio of at least 5.3:1, implying that it has significant internal cohesion. The color of the first interstellar planetesimal is at the neutral end of the range of Solar System $g-r$ and $r-J$ solar-reflectance colors: it is like that of some dynamically excited objects in the Kuiper belt and the less-red Jupiter Trojans.