  We present a cylindrically symmetric, Petrov type D, nonexpanding, shear free
and vorticity free solution of Einstein's field equations. The spacetime is
asymptotically flat radially and regular everywhere except on the symmetry axis
where it possesses a naked curvature singularity. The energy momentum tensor of
the spacetime is that for an anisotropic fluid which satisfies the different
energy conditions. This spacetime is used to generate a rotating spacetime
which admits closed timelike curves and may represent a Cosmic Time Machine.
