The source EUVE J1429-38.0 was discovered serendipitously by the Extreme Ultraviolet Explorer (EUVE) satellite on 1993 March 5. Optical spectroscopy confirms a cataclysmic variable--type optical counterpart for the source, showing Balmer, He I, and Ca emission, as well as strong He II emission. The optical spectrum, the apparent high/low state behavior, and possible weak cyclotron humps visible in the spectrum indicate that this star is likely to be an AM Herculis system, but the possibility of being a DQ Her, or an unlocked AM Her system, cannot be excluded. Analysis of the highly modulated EUVE photometry yields a period of 2 hr 22 minutes, which we conclude is the binary orbital period. In addition, a 57 minute period is also present. An orbital period of 2.5 hr would make EUVE J1429-38.0 only the third known AM Her system within the cataclysmic variable period gap, all three of which were discovered through EUV observations.