We present the results from exploratory Chandra observations of nine high-z (z=4.1-4.5) optically selected quasars. These quasars, taken from the DPOSS, are among the optically most luminous z>4 quasars known (M_B=-28.4 to -30.2). All have been detected by Chandra in exposure times of 5-6 ks, tripling the number of highly luminous quasars with X-ray detections at z>4. These quasars average broad-band SEDs are characterized by steeper aox values (<aox>=-1.81+/-0.03) than those of lower-luminosity, lower-redshift samples of quasars. We confirm the presence of a significant correlation between the UV magnitude and soft X-ray flux previously found for z>4 quasars. The joint 2-30 keV rest-frame X-ray spectrum of the nine quasars is well parameterized by a simple power-law model with Gamma=2.0+/-0.2, consistent with those of lower-z quasars. No evidence for significant amounts of intrinsic absorption has been found (N_H<8.8x10^21 cm^-2 at 90% confidence). In general, our results show that z=4.1-4.5 quasars and local quasars have reasonably similar X-ray and broad-band spectra (once luminosity effects are taken into account), suggesting that the accretion mechanisms in these objects are similar. We also present optical spectra for these quasars obtained with the HET; this is the first time optical spectra have been published for seven of these objects. The objects presented in this paper are among the best z>4 targets for X-ray spectroscopy with XMM-Newton and next-generation large-area X-ray telescopes. These will detect or constrain FeK_alpha emission lines down to rest-frame EWs of about 50 eV and intrinsic column densities down to N_H=a few x 10^21 cm^-2 at z=4. We also present 45 new ROSAT upper limits for z>4 quasars and a likely (3sigma) HRI detection of the blazar GB 1713+2148 at z=4.01.