  We calculate electric and magnetic form factors of protons and neutrons in
quenched Monte Carlo lattice QCD on a $16^3\times 24$ lattice at $\beta = 6.0$
using Wilson fermions. We employ a method which characterizes one of the
nucleon fields as a fixed zero-momentum secondary source. Extrapolating the
overall data set to the chiral limit, we find acceptable fits for either dipole
or monopole forms and extract proton and neutron magnetic moments, the
magnitude of which are $10$ to $15\%$ low compared to experiment. In the
extrapolation of the dipole fit of the form factors, we find that the dipole to
nucleon mass ratio is about $7\%$ low compared to experiment. In addition, we
obtain positive values of the neutron electric form factor, which, however, are
poorly represented by a popular phenomenological form at intermediate to small
$\kappa$ values. A zero-momentum technique for extracting hadron magnetic
moments is briefly discussed and shown to yield unrealistically small magnetic
moment values.
