Breakdown of Fourier law of heat conduction at nanometer length scales significantly diminishes thermal conductivity, leading to challenges in thermal management of nanoelectronic applications. In this work we demonstrate using first-principles computations that biaxial strain can enhance k at a nanoscale in boron phosphide (BP), yielding nanoscale k values that exceed even the bulk k value of silicon. At a length scale of L = 200 nm, k of 4% biaxially strained BP is enhanced by 25% to a value of 150.4 W m-1 K-1, relative to 120 W m-1 K-1 computed for unstrained BP at 300 K. The enhancement in k at a nanoscale is found to be due to the suppression of anharmonic scattering in the higher frequency range where phonon meanfreepaths are in nanometers, mediated by an increase in the phonon band gap in strained BP. Such a suppression in scattering enhances the meanfreepaths in the nanometer regime, thus enhancing nanoscale k. First-principles computations based on deriving harmonic and anharmonic force interactions from density-functional theory are used to provide detailed understanding of the effect in terms of individual scattering channels.