We present the discovery of a high-redshift, X-ray-selected active galactic nucleus (AGN) by the Calan-Yale Deep Extragalactic Research ( CYDER) survey: CXOCY J033716.7-050153, located at z=4.61, the second high-redshift AGN discovered by this survey. Here we present its optical, near-IR, and X-ray properties and compare it with other optical and X-ray-selected high-redshift AGNs. The optical luminosity of this object is significantly lower than most optically selected high-redshift quasars. It also has a lower rest-frame UV to X-ray emission ratio than most known quasars at this redshift. This mild deviation can be explained either by dust obscuring the UV radiation of a normal radio-quiet AGN emitting at 10% of its Eddington luminosity or because this is intrinsically a low-luminosity radio-loud AGN with a supermassive black hole of similar to10(8) M-circle dot emitting at 1% of its Eddington luminosity. Deep radio observations can discriminate between these two hypotheses.