  The problem of the statistics of a set of chaotic vortex lines in a
counterflowing superfluid helium is studied. We introduced a Langevin-type
force into the equation of motion of the vortex line in presence of relative
velocity $\mathbf{v_{ns}}$. This random force is supposed to be Gaussian
satisfying the fluctuation-dissipation theorem. The corresponding Fokker-Planck
equation for probability functional in the vortex loop configuration space is
shown to have a solution in the form of Gibbs distribution with the
substitution $E\{\mathbf{s\}\rightarrow }E(\{\mathbf{% s\}-P(v_{n}-v_{s})}$,
where $E\{\mathbf{s\}}$ is the energy of the vortex configuration
$\{\mathbf{s\}}$, and $\mathbf{P}$ is the Lamb impulse. Some physical
consequences of this fact are discussed.\\ \newline PACS numbers: 47.32.C-
(Vortex dynamics) 47.32.cf (Vortex reconnection and rings), 47.37.+q
(Hydrodynamic aspects of superfluidity)
