NGC 6334 is a galactic star-forming region in Scorpius, heavily obscured by intervening dust. The region consists of several major sites of star formation known previously from far-infrared (IR) and radio-wavelength observations. We present images of NGC 6334 obtained at wavelengths of 850 and 450 ensuremathmum with the Submillimeter Common-User Bolometric Array at the James Clerk Maxwell Telescope. These data highlight the distribution of dense cold dust, a particularly striking feature of which is a narrow ridge of emission passing between most of the star-forming centers. We use a clump-finding technique to quantify the distribution of dust emission throughout the region, and we obtain estimates of the sizes, masses, and temperatures of the clump ensemble under simple assumptions. Clump masses range from a minimum detectable of about 1 ensuremath Mensuremath<?iensuremath> ensuremath $ødot$ensuremath<?subensuremath>, up to almost 3000 ensuremath Mensuremath<?iensuremath> ensuremath $ødot$ensuremath<?subensuremath>. We find in particular that the ridge feature is characterized by a relatively narrow range of clump parameters as compared with the rest of NGC 6334, and we obtain a clump mass spectral index that lies between ensuremath N(M)ensuremath<?iensuremath> ? ensuremath Mensuremath<?iensuremath>ensuremath ?1.5ensuremath<?supensuremath> and ensuremath Mensuremath<?iensuremath>ensuremath ?1.0ensuremath<?supensuremath> for the high-mass clumps. The total mass of dust emitting at submillimeter wavelengths is about 16700 ensuremath Mensuremath<?iensuremath> ensuremath $ødot$ensuremath<?subensuremath> for an assumed temperature of 25 K; a significant fraction of this mass is contained within the ridge feature. These data are compared with recently published observations of NGC 6334 obtained at 1.2 mm wavelength using a direct-detection scanning technique, and with images obtained by the GLIMPSE-II and ensuremath Mid-course Space Experimentensuremath<?iensuremath> missions at wavelengths from 3.3 to 21 ensuremathmum in the near IR (NIR). The most massive compact submillimeter-wavelength regions in the north are invisible at these shorter wavelengths, and the NIR and mid-IR emission generally have little correspondence with the cool dust distribution. In this paper we use these data sets and supplementary millimeter-wavelength spectral line observations to investigate the star-forming sites in NGC 6334 and to speculate on the significance of the ridge of material seen in the submillimeter images.