Infrared absorption lines of H_3+, including the metastable R(3,3)l line, have been observed toward eight bright infrared sources associated with hot and massive stars located in and between the Galactic Center Cluster and the Quintuplet Cluster 30 pc to the east. The absorption lines with high velocity dispersion arise in the Galaxy's Central Molecular Zone (CMZ) as well as in foreground spiral arms. The temperature and density of the gas in the CMZ, as determined from the relative strengths of the H_3+ lines, are T=200 - 300 K and n<=50 - 200 cm-3. The detection of high column densities of H_3+ toward all eight stars implies that this warm and diffuse gaseous environment is widespread in the CMZ. The products of the ionization rate and path length for these sight lines are 1000 and 10 times higher than in dense and diffuse clouds in the Galactic disk, respectively, indicating that the ionization rate, \zeta, is not less than 10-15 s-1 and that L is at least on the order of 50 pc. The warm and diffuse gas is an important component of the CMZ, in addition to the three previously known gaseous environments: (1) cold molecular clouds observed by radio emission of CO and other molecules, (2) hot (T = 104 - 106 K) and highly ionized diffuse gas (ne = 10 - 100 cm-3) seen in radio recombination lines, far infrared atomic lines, and radio-wave scattering, and (3) ultra-hot (T = 107 - 108 K) X-ray emitting plasma. Its prevalence significantly changes the understanding of the environment of the CMZ. The sight line toward GC IRS 3 is unique in showing an additional H_3+ absorption component, which is interpreted as due to either a cloud associated with circumnuclear disk or the ``50 km s-1 cloud'' known from radio observations. An infrared pumping scheme is examined as a mechanism to populate the (3,3) metastable level in this cloud.