Ultracold polar molecules offer the possibility of exploring quantum gases with interparticle interactions that are strong, long-range, and spatially anisotropic. This is in stark contrast to the much studied dilute gases of ul- tracold atoms, which have isotropic and extremely short-range, or “contact”, interactions. Furthermore, the large electric dipole moment of polar molecules can be tuned with an external electric field; this provides unique opportuni- ties such as the control of ultracold chemical reactions [1], a unique platform for quantum information processing [2–4], and the realization of novel quantum many-body systems [5–8]. In spite of intense experimental efforts aimed at ob- serving the influence of dipoles on ultracold molecules [9], only recently have sufficiently high densities been achieved [10]. Here, we report the experimental observation of dipolar collisions in an ultracold molecular gas prepared close to quantum degeneracy. For modest values of an applied electric field, we observe a dramatic increase in the loss rate of fermionic KRb molecules due to ultrcold chemical reactions. We find that the loss rate has a steep power-law dependence on the induced electric dipole moment, and we show that this dependence can be understood with a relatively simple model based on quantum threshold laws for scattering of fermionic polar molecules. In addition, we directly observe the spatial anisotropy of the dipolar interaction as manifested in measurements of the thermodynamics of the dipolar gas. These results demonstrate how the long-range dipolar interaction can be used for electric-field control of chemical reaction rates in an ultracold polar molecule gas. Furthermore, the large loss rates in an applied electric field suggest that creating a long-lived ensemble of ultracold polar molecules may require confinement in a two-dimensional trap ge- ometry in order to suppress the influence of the attractive head-to-tail dipolar interactions [11–14]. Dipolar interactions have been explored in several atom gas experiments using the mag- netic dipole moments of atoms [15, 16], however this interaction is intrinsically orders of magnitude weaker than the dipolar interaction between typical polar molecules. Ultracold gases of polar molecules, then, open the possibility for realizing strong, and therefore rela- tively long-range, interactions. For example, with polar molecules confined in optical lattice potentials, one could realize a system where the interactions between particles in neighboring 2