  Recently, using the assumption that the string theory effective action at the
critical dimension is background independent, the classical on-shell effective
action of the bosonic string theory at order $\alpha'$ in a spacetime manifold
without boundary has been reproduced, up to an overall parameter, by imposing
the $O(1,1)$ symmetry when the background has a circle. In the presence of the
boundary, we consider a background which has boundary and a circle such that
the unit normal vector of the boundary is independent of the circle. Then the
$O(1,1)$ symmetry can fix the bulk action without using the lowest order
equation of motion. Moreover, the above constraints and the constraint from the
principle of the least action in the presence of boundary can fix the boundary
action, up to five boundary parameters. In the least action principle, we
assume that not only the values of the massless fields but also the values of
their first derivatives are arbitrary on the boundary.
  We have also observed that the cosmological/one-dimensional reduction of the
leading order action in the presence of the Hawking-Gibbons boundary term,
produces zero boundary action. Imposing this as another constraint on the
boundary couplings at order $\alpha'$, we find the boundary action up to two
parameters. For a specific value for these two parameters, the gravity
couplings in the boundary become the Chern-Simons gravity plus another term
which has the Laplacian of the extrinsic curvature.
