  We consider the integrable Camassa--Holm hierarchy on the line with positive
initial data rapidly decaying at infinity. It is known that flows of the
hierarchy can be formulated in a Hamiltonian form using two compatible Poisson
brackets. In this note we propose a new approach to Hamiltonian theory of the
CH equation. In terms of associated Riemann surface and the Weyl function we
write an analytic formula which produces a family of compatible Poisson
brackets. The formula includes an entire function $f(z)$ as a parameter. The
simplest choice $f(z)=1$ or $f(z)=z$ corresponds to the rational or
trigonometric solutions of the Yang-Baxter equation and produces two original
Poisson brackets. All other Poisson brackets corresponding to other choices of
the function $f(z)$ are new.
