We have combined first-principles and semiclassical Boltzmann transport theory to demonstrate the potential superb electronic and thermal transport properties of bulk and monolayer bismuth oxyiodide (BiOI). The exfoliation energy required to produce monolayer BiOI (22.53 meV/angstrom (2)) is lower than that required to produce monolayer h-BN, implying possible manufacturing from bulk. The calculated phonon frequencies, complemented with an ab initio molecular dynamic simulation for 8 ps at elevated temperature (900 K), reveal the monolayer’s dynamic and structural stability. The calculated band gaps are indirect for both bulk and monolayer and amount to 2.04 eV and 2.07 eV, respectively. Our results indicate remarkably high Seebeck coefficients for BiOI in the bulk (227 mu V/K at a hole concentration of 9.00 x 10(20) cm(-3)) and in the monolayer form (200 mu V/K at a hole concentration of 8.14 x 10(13) cm(-2)) at 900 K. The lowest lattice thermal conductivities of 1.35 W/mK for the bulk and 1.44 W/mK for the monolayer are obtained at 900 K. Because of the high value of S-2 sigma/tau for p-type doping, the figure of merit achieves peak values of 1.51 at a carrier concentration of 8.44 x 10(20) cm(-3) for bulk BiOI and 1.61 at a carrier concentration of 4.27 x 10(13) cm(-2) for monolayer BiOI.