Under the extreme condition of the scattering length being much shorter than the wavelength, light transport in random media is strongly modified by mesoscopic interference, and can even be halted in an effect known as Anderson localization. Anderson localization in three dimensions has recently been realized for acoustic waves and for cold atoms. Mats of disordered, high-refractive-index semiconductor nanowires are one of the strongest three-dimensional scattering materials for light, but localization has not been shown. Here, we use statistical methods originally developed for microwave waveguides to demonstrate that transport of light through nanowire mats is strongly correlated and governed by mesoscopic interference contributions. Our results confirm the contribution of only a few open modes to the transmission.