With ASCA, we found highly absorbed X-rays from the position of the bright transient source A1742-289, with variable flux ranging from 8*10^-12 to 4*10^-11 erg s^-1cm^-2 in the 3-10 keV band. We discovered an X-ray burst and eclipses from A1742-289, establishing that A1742-289 is an eclipsing low mass X-ray binary. Using the black body radius during the X-ray burst, we estimated the distance of A1742-289 to be about 10 kpc, or near the Galactic Center. Then the burst peak flux was found below the Eddington limit of a neutron star. Excess soft X-rays during the eclipse were detected, which are interpreted to be a scattering by interstellar dust-grains. Since A1742-289 was found to be an X-ray emitter even in the quiescent state with a moderate but variable flux, and since A1742-289 is lying only 1.3' from the Galactic center, previously reported X-ray fluxes of the Galactic center (Sgr A*) with non-imaging instruments might have been suffered by possible contamination of A1742-289.