  We propose a new way of second quantizing string theory. The method is based
on considering the Fock space of strings described by constituents which make
up the $X^\mu_R$ and the $X^\mu_L$ i.e. the right and left mover modes
separately. A state with any number of strings get represented by the Cartesian
product of two free particle Fock spaces, one for right mover degrees of
freedom, and one for left. The resulting string field theory is a free theory.
