  High precision radio-frequency, microwave and infrared spectroscopic
measurements of the antihydrogen molecular ion $\bar{H}_{2}^{-}$
($\bar{p}\bar{p}e^{+}$) compared with its normal matter counterpart provide
direct tests of the CPT theorem. The sensitivity to a difference between the
positron/antiproton and electron/proton mass ratios, and to a difference
between the positron-antiproton and electron-proton hyperfine interactions, can
exceed that obtained by comparing antihydrogen with hydrogen by several orders
of magnitude. Practical schemes are outlined for measurements on a single
$\bar{H}_{2}^{-}$ ion in a cryogenic Penning trap, that use non-destructive
state identification by measuring the cyclotron frequency and bound-positron
spin-flip frequency; and also for creating an $\bar{H}_{2}^{-}$ ion and
initializing its quantum state.
