The nucleon's strange-quark vector current form factors are studied from the
perspective of chiral symmetry. It is argued that chiral perturbation theory
cannot yield a prediction for the strangeness radius and magnetic moment.
Arrival at definite predictions requires the introduction of additional,
model-dependent assumptions which go beyond the framework of chiral
perturbation theory. A variety of such model predictions is surveyed, and the
credibility of each is evaluated. The most plausible prediction appears in a
model where the unknown chiral counterterms are identified with t-channel
vector meson exchange amplitudes. The corresponding prediction for the mean
square Dirac strangeness radius is ⟨rs2⟩=0.24 fm2, which
would be observable in up-coming semileptonic determinations of the nucleon's
strangeness form factors.Comment: LaTex 31 pages, four figures available from authors