Ne report optical spectroscopy and imaging of Tycho's supernova remnant (SNR) which suggest that two different precursors are associated with the blast wave. In long-slit spectra of the eastern rim, we find diffuse H alpha emission extending greater than or similar to 1' ahead of Knot g, a bright nonradiative shock propagating at velocity similar to 2000 km s(-1). In addition to the hydrogen lines, the diffuse spectrum also exhibits [S II] lambda lambda 6716, 6731; [N II] lambda 6583; and weak [O III] lambda 5007 emission. Narrowband imagery of Tycho's SNR shows that the diffuse emission extends ahead of most of the Balmer-dominated optical filaments and drops sharply in the remnant interior, suggesting that the diffuse gas is overrun by the supernova shock. The line ratios of the diffuse gas are compared with predictions from a simple He II lambda 304 photoionization precursor model. The models predict that the radiative transfer of He II lambda 304 photons in the precursor produces spatially distinct ionization layers of H-0, He-0-He+, N-0-N++,O-0-O++, and S+-S+3 ahead of the shock. The models suggest that the diffuse emission arises from collisional excitation in mostly neutral gas which has been heated to a temperature similar to 12,000 K. In high-resolution echelle spectra of Knot g, we find that the narrow H alpha component is broadened to 44 +/- 4 km s(-1), suggesting that the upstream gas may be further heated before it crosses the shock, perhaps by a fast neutral or cosmic-ray precursor. High-resolution spectroscopy of the H alpha line in both the diffuse region and Knot g will be required to definitively establish the existence of a second precursor.