  We investigate the chiral (flavor) structure of tetraquarks, and study chiral
transformation properties of the "non-exotic" [(3_bar,3)+(3,3_bar)] and
[(8,1)+(1,8)] tetraquark chiral multiplets. We find that as long as this kind
of tetraquark states contains one quark and one antiquark having the same
chirality, such as (q_L q_L \bar q_L \bar q_R + q_R q_R \bar q_R \bar q_L),
they transform in the same way as the lowest level (\bar q q) chiral multiplets
under chiral transformations. There is only one [(3_bar,3)+(3,3_bar)] chiral
multiplet whose quark-antiquark pairs all have the opposite chirality (q_L q_L
\bar q_R \bar q_R + q_R q_R \bar q_L \bar q_L), and it transforms differently
from others. Based on these studies, we construct local tetraquark currents
belonging to the "non-exotic" chiral multiplet [(3_bar,3)+(3,3_bar)] and having
quantum numbers J^{PC}=1^{-+}.
