We compute the leading contributions to the magnetic dipole and electr
ic quadrupole moments of the baryon decuplet in chiral perturbation th
eory. The measured value for the magnetic moment of the OMEGA- is used
to determine the local counterterm for the magnetic moments. We compa
re the chiral perturbation theory predictions for the magnetic moments
of the decuplet with those of the baryon octet and find reasonable ag
reement with the predictions of the large-N(c) limit of QCD. The leadi
ng contribution to the quadrupole moment of the DELTA and other member
s of the decuplet comes from one-loop graphs. The pionic contribution
is shown to be proportional to I(z) (and so will not contribute to the
quadrupole moment of I = 0 nuclei), while the contribution from kaons
has both isovector and isoscalar components. The chiral logarithmic e
nhancement of both pion and kaon loops has a coefficient that vanishes
in the SU(6) limit. The third allowed moment, the magnetic octupole,
is shown to be dominated by a local counterterm with corrections arisi
ng at two loops. We briefly mention the strange counterparts of these
moments.