The B(1/2 P-2(3/2))-->X(1/2 (2) Sigma(+)) transition in XeI (2385-2490 Angstrom) is recorded at high resolution for the single isotopomer (XeI)-Xe-136-I-127, using a Tesla discharge source and a CCD array detector. The high signal-to-noise capabilities of the detector make it possible to measure the discrete vibrational structure in this system for the first time. The assignments consist of 86 v’-v" bands spanning 15 upper-state levels (assigned as v’=3-17) and 17 lower-state levels (tentatively assigned as v"=0-16). A vibrational analysis yields the following spectroscopic constants (cm(-1)) : Delta T-e=40 047.8, omega(e)’ = 110.6, omega(e)x(e)’ = 0.217, omega(e)" = 24.0, omega(e)x(e)" = 0.66. From a near-dissociation analysis, the X state has a dissociation energy (D-e) of 267+/-5 cm(-1) and supports 28 bound vibrational levels. However, it is likely that our lowest observed v" level is not v"=O, so these values should be considered lower limits. The potential energy curves are modeled by a Morse-RKR function for the X state and a Rittner function for the B state. Trial-and-error Franck-Condon calculations are used to locate the B- and X-state potential curves relative to each other, fixing the X-state internuclear distance R(e) at a value similar to 0.7 Angstrom larger than that for the B state. Bound-free simulations of the low-resolution spectrum indicate that the X potential must be significantly steeper in the Franck-Condon region than found from previous scattering studies.