We present the first image of the thermal Sunyaev-Zel'dovich effect (SZE) obtained by the Atacama Large Millimeter/submillimeter Array (ALMA). Combining 7-m and 12-m arrays in Band 3, we create an SZE map toward a galaxy cluster RX J1347.5-1145 with 5″ resolution (corresponding to a physical size of 20 h$^-1$ kpc), the highest angular and physical spatial resolutions achieved to-date for imaging the SZE, while retaining extended signals out to 40″. The 1 \ensuremathσ statistical sensitivity of the image is 0.017 mJy beam$^-1$ or 0.12 mK$_CMB$ at the 5″ full width at half maximum. The SZE image shows a good agreement with an electron pressure map reconstructed independently from the X-ray data and offers a new probe of the small-scale structure of the intracluster medium. Our results demonstrate that ALMA is a powerful instrument for imaging the SZE in compact galaxy clusters with unprecedented angular resolution and sensitivity. As the first report on the detection of the SZE by ALMA, we present detailed analysis procedures including corrections for the missing flux, to provide guiding methods for analyzing and interpreting future SZE images obtained by ALMA.