  The muon-capture reactions 2H(\mu^-,\nu_\mu)nn and 3He(\mu^-,\nu_\mu)3H are
studied with nuclear strong-interaction potentials and charge-changing weak
currents, derived in chiral effective field theory. The low-energy constants
(LEC's) c_D and c_E, present in the three-nucleon potential and (c_D)
axial-vector current, are constrained to reproduce the A=3 binding energies and
the triton Gamow-Teller matrix element. The vector weak current is related to
the isovector component of the electromagnetic current via the
conserved-vector-current constraint, and the two LEC's entering the contact
terms in the latter are constrained to reproduce the A=3 magnetic moments. The
muon capture rates on deuteron and 3He are predicted to be 399(3) sec^{-1} and
1494 (21) sec^{-1}, respectively, where the spread accounts for the cutoff
sensitivity as well as uncertainties in the LEC's and electroweak radiative
corrections. By comparing the calculated and precisely measured rates on 3He, a
value for the induced pseudoscalar form factor is obtained in good agreement
with the chiral perturbation theory prediction.
