We present sensitive, high angular resolution molecular line observations of C¹⁸O and N₂H⁺ toward the dark globule B68. We directly compare these data with the near-infrared extinction measurements of Alves, Lada, & Lada to derive the first evidence for the depletion of N₂H⁺, and by inference N₂, in a prestellar dark cloud. We also find widespread C¹⁸O depletion throughout the centrally condensed core of the B68 cloud. Specifically, we find the N₂H⁺ emission to peak in a shell partially surrounding the peak of dust extinction. Moreover, N₂H⁺ peaks inside the much larger C¹⁸O depletion hole and has a smaller depletion zone, confirming theoretical predictions. These data are analyzed through a direct coupling of time-dependent chemical models to a radiation transfer code. This analysis highlights the importance of photodissociation at cloud edges and suggests that the CO abundance declines by 2 orders of magnitude from edge to center. In contrast, N₂H⁺ declines in abundance, at minimum, by at least a factor of 2. Indeed, it is entirely possible that both N₂H⁺ and N₂ are completely absent from the central regions of the B68 core. The depletion of N₂H⁺, and its parent molecule N₂, opens up the possibility that the centers of dense cores, prior to the formation of a star, may evade detection by conventional methods of probing cores using molecular emission. Under these conditions, H₂D⁺ may be the sole viable molecular probe of the innermost regions of star-forming cores.