Fluid jets are found in nature at all length scales from microscopic to cosmological. Here we report on an electroosmotically driven jet from a single glass nanopore about 75 nm in radius with a maximum flow rate ~15 pL/s. A novel anemometry technique allows us to map out the vorticity and velocity fields that show excellent agreement with the classical Landau-Squire solution of the Navier-Stokes equations for a point jet. We observe a phenomenon that we call flow rectification: an asymmetry in the flow rate with respect to voltage reversal. Such a nanojet could potentially find applications in micromanipulation, nanopatterning, and as a diode in microfluidic circuits.