Abstract: A measurement of the shape of the differential decay rate and the associated Isgur-Wise function for the decay Lambda(0)(b) ->+ Lambda(+)(c) mu(-) is reported, using data corresponding to 3 fb(-1) collected with the LHCb detector in proton-proton collisions. The Lambda(+)(c) mu(-)(nu) over bar μ(+anything) final states are reconstructed through the detection of a muon and Lambda(+)(c) baryon decaying into pK(-)pi(+), and the decay Lambda(0)(b) -> Lambda(+)(c)pi(+)pi(-)mu(-)(nu) over bar μare used to determine contributions from Lambda(0)(b) -> Lambda(c)*(+)mu(-)(nu) over bar μdecays. The measured dependence of the differential decay rate upon the squared four-momentum transfer between the heavy baryons, q(2), is compared with expectations from heavy-quark effective theory and from unquenched lattice QCD predictions.