  The successful description of current data provided by the Standard Model
includes fundamental fermions that are color-singlets and
electroweak-nonsinglets, but no fermions that are electroweak-singlets and
color-nonsinglets. In an effort to understand the absence of such fermions, we
construct and study {\it gedanken} models that do contain electroweak-singlet
chiral quark fields. These models exhibit several distinctive properties,
including the absence of any neutral lepton and the fact that both the $(uud)$
and $(ddu)$ nucleons are electrically charged. We also explore how such models
could arise as low-energy limits of grand unified theories and, in this more
restrictive context, we show that they exhibit further exotic properties.
