  We propose the pure sea-quark contributions to the magnetic form factors of
$\Sigma$ baryons, $G_{\Sigma^-}^u$ and $G_{\Sigma^+}^d$, as priority
observables for the examination of sea-quark contributions to baryon structure,
both in present lattice QCD simulations and possible future experimental
measurement. $G_{\Sigma^-}^u$, the $u$-quark contribution to the magnetic form
factor of $\Sigma^-$, and $G_{\Sigma^+}^d$, the $d$-quark contribution to the
magnetic form factor of $\Sigma^+$, are similar to the strange quark
contribution to the magnetic form factor of the nucleon, but promise to be
larger by an order of magnitude. We explore the size of this quantity within
chiral effective field theory, including both octet and decuplet intermediate
states. The finite range regularization approach is applied to deal with
ultraviolet divergences. Drawing on an established connection between quenched
and full QCD, this approach makes it possible to predict the sea quark
contribution to the magnetic form factor purely from the meson loop. In the
familiar convention where the quark charge is set to unity $G_{\Sigma^-}^u =
G_{\Sigma^+}^d$. We find a value of $-0.38^{+0.16}_{-0.17}\ \mu_N$, which is
about seven times larger than the strange magnetic moment of the nucleon found
in the same approach. Including quark charge factors, the $u$-quark
contribution to the $\Sigma^-$ magnetic moment exceeds the strange quark
contribution to the nucleon magnetic moment by a factor of 14.
