At 22:42:31 UT, the Swift Burst Alert Telescope (BAT) triggered and located IGR J17062-6143 (trigger=525148). Swift slewed immediately to the source. The BAT on-board calculated location is RA, Dec 256.609, -61.728 which is RA(J2000) = 17h 06m 26s Dec(J2000) = -61d 43' 40" with an uncertainty of 3 arcmin (radius, 90% containment, including systematic uncertainty). As is typical with image triggers (duration = 64 sec), the real-time lightcurve does not show anything significant. The XRT began observing the field at 22:45:05.2 UT, 153.6 seconds after the BAT trigger. XRT found a bright X-ray source located at RA, Dec 256.5681, -61.7098 which is equivalent to: RA(J2000) = +17h 06m 16.34s Dec(J2000) = -61d 42' 35.3" with an uncertainty of 5.7 arcseconds (radius, 90% containment). This location is 95 arcseconds from the BAT onboard position, within the BAT error circle. No event data are yet available to determine the column density using X-ray spectroscopy. The initial flux in the 0.1 s image was 2.25e-08 erg cm^-2 s^-1 (0.2-10 keV). UVOT took a finding chart exposure of 250 seconds with the U filter starting 321 seconds after the BAT trigger. There is a candidate afterglow in the rapidly available 2.7'x2.7' sub-image at RA(J2000) = 17:06:16.27 = 256.56779 DEC(J2000) = -61:42:40.0 = -61.71112 with a 90%-confidence error radius of about 0.61 arc sec. This position is 4.8 arc sec. from the center of the XRT error circle. The estimated magnitude is 15.84 with a 1-sigma error of about 0.14. No correction has been made for the expected extinction corresponding to E(B-V) of 0.15. IGR J17062-6143 is a known X-ray transient with a location of RA=256.56771, DEC=-61.71125 (RA=17 06 16.3, DEC=-61 42 40.5) with an uncertainty of 0.3 arc sec (ATEL #1840; Ricci et al.), consistent with this detection. The nature of this transient is unknown and further observation are warranted.