We present molecular line mapping of the Giant Molecular Cloud G1.6-0.025, which is located at the high longitude end of the Central Molecular Zone of our Galaxy. We assess the degree of star formation activity in that region using several tracers and find very little. We made a large scale, medium (2) resolution map in the J = 2-1 transition of SiO for which we find clumpy emission over a ~0.8 x 0.3 degree-sized region stretching along the Galactic plane. Toward selected positions we also took spectra in the easy to excite J_k=2_k-1_k quartet of CH3OH and the CS 2-1 line. Throughout the cloud these meth lines are, remarkably, several times stronger than, both, the CS and the SiO lines. The large widths of all the observed lines, similar to values generally found in the Galactic center, indicate a high degree of turbulence. Several high LSR velocity clumps that have 0-80 km/s higher velocities than the bulk of the molecular cloud appear at the same projected position as normal velocity material; this may indicate cloud-cloud collisions. Statistical equilibrium modeling of the CH3OH lines observed by us and others yield relatively high densities and moderate temperatures for a representative dual velocity position. We find 8 10^4 cm-3/30 K for material in the G1.6-0.025 cloud and a higher temperature (190 K), but a 50% lower density in a high velocity clump projected on the same location. Several scenarios are discussed in which shock chemistry might enhance the CH3OH and SiO abundances in G1.6-0.025 and elsewhere in the Central Molecular Zone.