  A new set of boundary conditions for string propagators is proposed in this
paper. The boundary conditions are parametrized by a complex number $\lambda$.
Under these new boundary conditions, the left-moving and right-moving modes are
treated unequally. Thus, we called them chiral string theories. If $\lambda =
-1$, the spectrum of such theory truncates to a finite number, and therefore it
becomes a different description of supergravity. We found the spectrum of
chiral string theories by requiring that the vertex operators are conformally
invariant. In addition, we also calculate the amplitudes for arbitrary
$\lambda$. The amplitudes are expressed as a product of open string amplitudes
which are similar to the KLT relation. The unitarity of these theories are
investigated. However, we found out that except for $\lambda = \pm 1$, all
other theories are not unitary; i.e., only the supergravity and ordinary
strings are unitary. Although most of the chiral strings are not physical, they
still serve as a valuable tool in studying the relation between particle
theories and string theories.
