In this paper, we report accurate Chandra positions for two ultraluminous X-ray sources (ULXs): NGC 7319-X4 at Right Ascension (RA) = 339029 17(2), Declination (Dec.) = 33974 76(2) and NGC 5474-X1 at RA = 211248 59(3), Dec. = 53635 84(3). We perform bore-sight corrections on the Chandra X-ray satellite observations of these sources to get these accurate positions of the X-ray sources and match these positions with archival optical data from the Wide Field Planetary Camera 2 (WFPC2) onboard the Hubble Space Telescope. We do not find the optical counterparts; the limiting absolute magnitudes of the observations in the WFPC2 standard magnitude system are B=−7.9, V=−8.7 and I=−9.3 for NGC 7319-X4 and U=−6.4 for NGC 5474-X1. We report on the X-ray spectral properties and find evidence for X-ray variability in NGC 5474-X1. Finally, we briefly discuss several options for the nature of these ULXs.