  The thermodynamic properties of the (2+1)-dimensional non-rotating black hole
of Ba\~nados, Teitelboim and Zanelli are discussed. The first quantum
correction to the Bekenstein-Hawking entropy is evaluated within the on-shell
Euclidean formalism, making use of the related Chern-Simons representation of
the 3-dimensional gravity. Horizon and ultraviolet divergences in the quantum
correction are dealt with a renormalization of the Newton constant. It is
argued that the quantum correction due to the gravitational field shrinks the
effective radius of a hole and becomes more and more important as soon as the
evaporation process goes on, while the area law is not violated.
