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The central molecular zone (CMZ) of our Galaxy exhibits widespread emission from SiO and various complex organic molecules (COMs), yet the exact origin of such emission is uncertain. Here we report the discovery of a unique class of long ($>$0.5 pc) and narrow ($<$0.03 pc) filaments in the emission of SiO 5$-$4 and eight additional molecular lines, including several COMs, in our ALMA 1.3 mm spectral line observations toward two massive molecular clouds in the CMZ, which we name as slim filaments. However, these filaments are not detected in the 1.3 mm continuum at the 5$\sigma$ level. Their line-of-sight velocities are coherent and inconsistent with being outflows. The column densities and relative abundances of the detected molecules are statistically similar to those in protostellar outflows but different from those in dense cores within the same clouds. Turbulent pressure in these filaments dominates over self gravity and leads to hydrostatic inequilibrium, indicating that they are a different class of objects than the dense gas filaments in dynamical equilibrium ubiquitously found in nearby molecular clouds. We argue that these newly detected slim filaments are associated with parsec-scale shocks, likely arising from dynamic interactions between shock waves and molecular clouds. The dissipation of the slim filaments may replenish SiO and COMs in the interstellar medium and lead to their widespread emission in the CMZ., Comment: 14 pages, 9 figures, 2 tables