  In the sigma model approach, the $\beta$-function equations for non critical
strings contain a term which acts like a tree level cosmological constant,
$\Lambda$. We analyse the static, spherically symmetric solutions to these
equations in $d = 4$ space time and show that the curvature scalar seen by the
strings is singular if $\Lambda \ne 0$. This singularity is naked. Requiring
its absence in our universe imposes the constraint $| \Lambda | < 10^{- 120}$
in natural units. {}From another point of view, our analysis implies that low
energy $d = 4$ non critical strings lead to naked singularities.
