  We investigate higher loop integrability for a q-deformation of the
su(2)-sector of N=4 SYM theory. First we construct a generalisation of the long
range spin chain, which for the lowest orders describes the non-deformed
dilatation operator. This generalised model is built up from Temperley-Lieb
algebra generators and describes the deformed theory to at least two loops.
When constructing the model we have demanded the existence of one commuting
charge, which puts strong constraints on the parameters to three loop orders.
We also write down the five first charges for this model at two loops order.
Our main goal is to obtain an explicit expression for an infinite number of
commuting charges, all commuting with the dilatation operator. This would imply
integrability. As a step towards this goal we present in this paper an
expression for a generic local charge of the one-loop dilatation operator,
which happens to be a generator of the Temperley-Lieb algebra.
