The iron antimonide FeSb2 possesses an extraordinarily high thermoelectric power factor at low temperature, making it a leading candidate for cryogenic thermoelectric cooling devices. However, the origin of this unusual behavior is controversial, having been variously attributed to electronic correlations as well as the phonon-drag effect. The optical properties of a material provide information on both the electronic and vibrational properties. The optical conductivity reveals an anisotropic response at room temperature; the low-frequency optical conductivity decreases rapidly with temperature, signalling a metal-insulator transition. One-dimensional semiconducting behavior is observed along the b axis at low temperature, in agreement with first-principle calculations. The infrared-active lattice vibrations are also symmetric and extremely narrow, indicating long phonon relaxation times and a lack of electron-phonon coupling. Surprisingly, there are more lattice modes along the a axis than are predicted from group theory; several of these modes undergo significant changes below about 100 K, hinting at a weak structural distortion or phase transition. While the extremely narrow phonon line shapes favor the phonon-drag effect, the one-dimensional behavior of this system at low temperature may also contribute to the extraordinarily high thermopower observed in this material.