Cold antihydrogen is produced when antiprotons are repeatedly driven into collisions with cold positrons within a nested Penning trap. Efficient antihydrogen production takes place during many cycles of positron cooling of antiprotons. A first measurement of a distribution of antihydrogen states is made using a preionizing electric field between separated production and detection regions. Surviving antihydrogen is stripped in an ionization well that captures and stores the freed antiproton for background-free detection.