  We study a special two-dimensional dilaton gravity with Lagrangian
$\mathcal{L}=\frac{1}{2}\sqrt{-g}(\phi R+{\lambda^2}{\rm sech}^2\phi)$ where
$\lambda$ is a parameter of dimension mass. This theory describes
two-dimensional spacetimes that are asymptotically flat. Very interestingly, it
has an exact solution for the metric, $\d s^2=-(c+\tanh \lambda x)\d t^2+ \d
x^2/(c+\tanh {\lambda} x)$, parametrized by $c$. For $c\in(-1,1)$, the solution
presents an event horizon but no singularity. Because of the kink profile for
the metric components appearing in the solution, we refer to the spacetime
described by the metric as a {\it gravitational domain wall} with the wall
simply being the event horizon and separating two asymptotically Minkowskian
spacetimes. The global causal structure for such an object is studied via
coordinate extension and the thermodynamical quantities are computed. Only when
$c\in(-1,0]$ are the entropy and energy non-negative.
