The production of neutron beams having short temporal duration is studied using ultraintense laser pulses. Laser-accelerated protons are spectrally filtered using a laser-triggered microlens to produce a short duration neutron pulse via nuclear reactions induced in a converter material (LiF). This produces a ∼3  ns duration neutron pulse with 10(4)  n/MeV/sr/shot at 0.56 m from the laser-irradiated proton source. The large spatial separation between the neutron production and the proton source allows for shielding from the copious and undesirable radiation resulting from the laser-plasma interaction. This neutron pulse compares favorably to the duration of conventional accelerator sources and should scale up with, present and future, higher energy laser facilities to produce brighter and shorter neutron beams for ultrafast probing of dense materials.