We report the discovery of an extremely luminous galaxy lying at a redshift of z=5.74, SSA22-HCM1. The object was found in narrowband imaging of the SSA22 field using a 105 Angstrom bandpass filter centered at 8185 Angstroms during the course of the Hawaii narrowband survey using LRIS on the 10 m Keck II Telescope, and was identified by the equivalent width of the emission W_lambda(observed)=175 Angstroms, flux = 1.7 x 10^{-17} erg cm^{-2} s^{-1}). Comparison with broadband colors shows the presence of an extremely strong break (> 4.2 at the 2 sigma level) between the Z band above the line, where the AB magnitude is 25.5, and the R band below, where the object is no longer visible at a 2 sigma upper limit of 27.1 (AB mags). These properties are only consistent with this object's being a high-z Ly alpha emitter. A 10,800 s spectrum obtained with LRIS yields a redshift of 5.74. The object is similar in its continuum shape, line properties, and observed equivalent width to the z=5.60 galaxy, HDF 4-473.0, as recently described by Weymann et al. (1998), but is 2-3 times more luminous in the line and in the red continuum. For H_0 = 65 km s^{-1} Mpc^{-1} and q_0 = (0.02, 0.5) we would require star formation rates of around (40, 7) solar masses per year to produce the UV continuum in the absence of extinction.