We report our 110 ks Chandra observations of the supernova remnant (SNR) 0104-72.3 in the Small Magellanic Cloud (SMC). The X-ray morphology shows two prominent lobes along the northwest-southeast direction and a soft faint arc in the east. Previous low resolution X-ray images attributed the unresolved emission from the southeastern lobe to a Be/X-ray star. Our high resolution Chandra data clearly shows that this emission is diffuse, shock-heated plasma, with negligible X-ray emission from the Be star. The eastern arc is positionally coincident with a filament seen in optical and infrared observations. Its X-ray spectrum is well fit by plasma of normal SMC abundances, suggesting that it is from shocked ambient gas. The X-ray spectra of the lobes show overabundant Fe, which is interpreted as emission from the reverse-shocked Fe-rich ejecta. The overall spectral characteristics of the lobes and the arc are similar to those of Type Ia SNRs, and we propose that SNR 0104-72.3 is the first case for a robust candidate Type Ia SNR in the SMC. On the other hand, the remnant appears to be interacting with dense clouds toward the east and to be associated with a nearby star-forming region. These features are unusual for a standard Type Ia SNR. Our results suggest an intriguing possibility that the progenitor of SNR 0104-72.3 might have been a white dwarf of a relatively young population.