  The Colours of the Outer Solar System Origins Survey (Col-OSSOS) is acquiring
near-simultaneous $g$, $r$, and $J$ photometry of unprecedented precision with
the Gemini North Telescope, targeting nearly a hundred trans-Neptunian objects
(TNOs) brighter than $m_r=23.6$ mag discovered in the Outer Solar System
Origins Survey. Combining the optical and near-infrared photometry with the
well-characterized detection efficiency of the Col-OSSOS target sample will
provide the first flux-limited compositional dynamical map of the outer Solar
System. In this paper, we describe our observing strategy and detail the data
reduction processes we employ, including techniques to mitigate the impact of
rotational variability. We present optical and near-infrared colors for 35
TNOs. We find two taxonomic groups for the dynamically excited TNOs, the
neutral and red classes, which divide at $g-r \simeq 0.75$. Based on simple
albedo and orbital distribution assumptions, we find that the neutral class
outnumbers the red class, with a ratio of 4:1 and potentially as high as 11:1.
Including in our analysis constraints from the cold classical objects, which
are known to exhibit unique albedos and $r-z$ colors, we find that within our
measurement uncertainty, our observations are consistent with the primordial
Solar System protoplanetesimal disk being neutral-class-dominated, with two
major compositional divisions in $grJ$ color space.
