  Motivated by excess diphoton events reported by ATLAS and CMS, we show that
composite pseudoscalars, bound states of heavy fermions under a new confining
gauge theory, can be pair-produced by Drell-Yan production if the constituent
particles are electrically charged. The decays of these pion-like bound states
into two photons can explain the observed events near 750 GeV. The model
predicts that there should be significant numbers of 4-photon events from
decays of the pseudoscalar pairs, as well as same-sign dilepton pairs at a
somewhat lower invariant mass, or multijet signals, coming from decays of
charge-2 pseudoscalars. These states and their decays are necessary for
avoiding stable charged baryon-like relics in the new confining sector. A
neutral baryon-like dark matter candidate of mass $\sim N_c\times 375$ GeV is a
further prediction of the model, for SU($N_c$) confining gauge group.
