It can be generally argued that the presumably adequate family symmetry should be chiral rather than vectorlike, since the vectorlike family symmetries do not in general forbid the large invariant masses for quark-lepton families. This may lead (without some special fine tuning of parameters) to the almost uniform mass spectra for them that would be natural if the family symmetry were exact rather than broken. Rather intriguingly, both known examples of the local vectorlike symmetries, electromagnetic U ( 1 ) E M and color S U ( 3 ) C , appear to be exact symmetries, while all chiral symmetries including the conventional electroweak symmetry S U ( 2 ) W × × U ( 1 ) Y and grand unifications SU(5), SO(10) and E(6) appear broken. In this connection, one of the most potentially relevant option considered in the literature may be associated with the local chiral S U ( 3 ) F family symmetry introduced by Chkareuli in 1980 in the framework of the family-unified S U ( 8 ) symmetry and further developed by its own.