A study of the associated production of a Z boson and a charm quark jet ( Z + c ), and a comparison to production with a b quark jet ( Z + b ), in p p collisions at a centre-of-mass energy of 8 TeV are presented. The analysis uses a data sample corresponding to an integrated luminosity of 19.7 fb - 1 , collected with the CMS detector at the CERN LHC. The Z boson candidates are identified through their decays into pairs of electrons or muons. Jets originating from heavy flavour quarks are identified using semileptonic decays of c or b flavoured hadrons and hadronic decays of charm hadrons. The measurements are performed in the kinematic region with two leptons with p T ℓ > 20 GeV , | η ℓ | < 2.1 , 71 < m ℓ ℓ < 111 GeV , and heavy flavour jets with p T jet > 25 GeV and | η jet | < 2.5 . The Z + c production cross section is measured to be σ ( p p → Z + c + X ) B ( Z → ℓ + ℓ - ) = 8.8 ± 0.5 (stat) ± 0.6 (syst) pb . The ratio of the Z + c and Z + b production cross sections is measured to be σ ( p p → Z + c + X ) / σ ( p p → Z + b + X ) = 2.0 ± 0.2 (stat) ± 0.2 (syst) . The Z + c production cross section and the cross section ratio are also measured as a function of the transverse momentum of the Z boson and of the heavy flavour jet. The measurements are compared with theoretical predictions.