We report on the result of a search for an X-ray counterpart to the peculiar gamma-ray burst of 1994 February 17 (GRB 940217) detected with the ASCA satellite. This was one of the strongest bursts detected by BATSE onboard CGRO. Furthermore, it had the longest duration (90 min); and the hardest gamma-ray emission (similar to 18 GeV) of all GRBs observed so far. Three pointed observations with ASCA were performed to cover the error region determined by the EGRET (95% confidence level), COMPTEL (3 sigma confidence level), and the Interplanetary Network (TPN) localization. We detected one X-ray source (2-10 keV flux: 3.7 x 10(-13) erg s(-1) cm(-2)) within the error region. Using the APM system at the Royal Greenwich Observatory, we found two optical sources within 1' of this source. One of the optical sources has a B-R color consistent with an AGN. The implied optical-to-X ray flux ratio is also reasonable for an AGN. If the X-ray source is an AGN with a luminosity of 10(45) erg s(-1) (4.7 Gpc; z = 1) and is the source of the burst, a lower limit on the relativistic bulk Lorentz beaming factor, greater than or similar to 50, can be derived from the energy spectra and fine-time structure observed by COMPTEL.