  We describe integrable elliptic q-deformed anisotropic long-range spin chain.
The derivation is based on our recent construction for commuting anisotropic
elliptic spin Ruijsenaars-Macdonald operators. We prove that the Polychronakos
freezing trick can be applied to these operators, thus providing the commuting
set of Hamiltonians for long-range spin chain constructed by means of the
elliptic Baxter-Belavin ${\rm GL}_M$ $R$-matrix. Namely, we show that the
freezing trick is reduced to a set of elliptic function identities, which are
then proved. These identities can be treated as conditions for equilibrium
position in the underlying classical spinless Ruijsenaars-Schneider model.
Trigonometric degenerations are studied as well. For example, in $M=2$ case our
construction provides q-deformation for anisotropic XXZ Haldane-Shastry model.
The standard Haldane-Shastry model and its Uglov's q-deformation based on ${\rm
U}_q({\widehat {\rm gl}_M})$ XXZ $R$-matrix are included into consideration by
separate verification.
