  The stabilisation by noise on the boundary of the Chafee-Infante equation
with dynamical boundary conditions subject to a multiplicative It\^o noise is
studied. In particular, we show that there exists a finite range of noise
intensities that imply the exponential stability of the trivial steady state.
This differs from previous works on the stabilisation by noise of parabolic
PDEs, where the noise acts inside the domain and stabilisation typically occurs
for an infinite range of noise intensities. To the best of our knowledge, this
is the first result on the stabilisation of PDEs by boundary noise.
