  We study a class of disordered continuous classical spin systems including
the kagome Heisenberg magnet. While each term in its local Hamiltonian can be
independently minimised, we find {\it discrete} degenerate ground states whose
number grows exponentially with system size. These states do not exhibit
zero-energy `excitations' characteristic of highly frustrated magnets but
instead are local minima of the energy landscape, albeit with an anomalously
soft excitation spectrum. This represents a spin liquid version of the
phenomenon of jamming familiar from granular media and structural glasses.
Correlations of this jammed spin liquid, which upon increasing the disorder
strength gives way to a conventional spin glass, may be algebraic
(Coulomb-type) or exponential.
