The Chandra High Resolution Camera observed the fields of five hard X-ray sources in order to help us obtain X-ray coordinates with sub-arcsecond precision. These observations provide the most accurate X-ray positions known for IGR J16393-4643 and for IGR J17091-3624. The obscured X-ray pulsar IGR J16393-4643 lies at R.A. (J2000) = 16:39:05.47, and Dec. = -46:42:13.0 (error radius of 0.6" at 90% confidence). This position is incompatible with the previously-proposed counterpart 2MASS J16390535-4642137, and it points instead to a new counterpart candidate that is possibly blended with the 2MASS star. The black hole candidate IGR J17091-3624 was observed during its 2011 outburst providing coordinates of R.A. = 17:09:07.59, and Dec. = -36:24:25.4. This position is compatible with those of the proposed optical/IR and radio counterparts, solidifying the source's status as a microquasar. Three targets, IGR J14043-6148, IGR J16358-4726, and IGR J17597-2201, were not detected. We obtained 3{\sigma} upper limits of, respectively, 1.7, 1.8, and 1.5 \times 10^-12 erg cm^-2 s^-1 on their 2-10 keV fluxes.