This paper describes observations of PC 1247 + 3406, a quasar with a redshift of 4.897 +/- 0.011. The redshift is based on three strong emission lines and the presence of substantial absorption, presumably due to "Lyman alpha clouds," on the blue side of the Lyman alpha emission line. The quasar is about the same brightness as PC 1158 + 4635, the 20th magnitude z = 4.733 quasar found in 1989. PC 1247 + 3406 was discovered in a four-filter CCD survey designed to detect quasars with redshifts between 4.0 and 5.5. The properties of PC 1247 + 3406 seem quite similar to other z > 3 quasars, although the absorption due to intervening neutral hydrogen is almost-equal-to 20% less than expected. The flux in the spectrum abruptly drops at a wavelength of almost-equal-to 910 A in the rest frame of the quasar. This quick encounter with a Lyman-limit system is frequently seen in other z > 4.3 quasars.