  We calculate electromagnetic neutral pion production off tri-nucleon bound
states (3H, 3He) at threshold in chiral nuclear effective field theory to
fourth order in the standard heavy baryon counting. We show that the fourth
order two-nucleon corrections to the S-wave multipoles at threshold are very
small. This implies that a precise measurement of the S-wave cross section for
neutral pion production off 3He allows for a stringent test of the chiral
perturbation theory prediction for the S-wave electric multipole E_{0+}^{pi0
n}.
