A large scale C^18O(J=1-0) survey of the central few hundred pc (-1.05^o <= l <= +3.6^o, -0.9^o <= b <= +0.75^o) of the Galaxy is presented. These 9^' resolution data were obtained with the 1.2 m Southern Millimeter-Wave Telescope (SMWT) at CTIO and compared to ^12CO(1-0) data also obtained with this telescope. In addition, HNCO(5_0,5-4_0,4) line data included in the spectrometer passband are also presented. Although both ^12CO and C^18O are thought to be tracers of the molecular mass, their distribution and line shapes differ significantly. The C^18O(1-0) line is mucher weaker than expected from the ``Standard I_^12CO(1-0)/N_H_2 Conversion Formula'' obtained by Strong et al. (1988). LVG calculations suggest that on large scales the ^12CO(1-0) emission is only of intermediate ( tau = 1 - 5) or low optical depth ( tau < 1). In this case, the ``Standard Conversion Formula'' overestimates N_H_2. Our C^18O(1-0) data combined with other H_2 tracers indicate a total molecular mass of (3^+2_-1) * 10^7 M_o. The existence of a widespread component of molecular gas with low density (thin gas) is found to be very likely.