  Channel linear Weingarten surfaces in space forms are investigated in a Lie
sphere geometric setting, which allows for a uniform treatment of different
ambient geometries. We show that any channel linear Weingarten surface in a
space form is isothermic and, in particular, a surface of revolution in its
ambient space form. We obtain explicit parametrisations for channel surfaces of
constant Gauss curvature in space forms, and thereby for a large class of
linear Weingarten surfaces up to parallel transformation.
