Heavy quark production in 7 TeV centre-of-mass energy pp collisions at the LHC is not necessarily flavour symmetric. The production asymmetry, A_P, between Ds+ and Ds- mesons is studied using the phi pi(+/-) decay mode in a data sample of 1.0/fb collected with the LHCb detector. The difference between pi+ and pi- detection efficiencies is determined using the ratios of fully reconstructed to partially reconstructed D*(+/-) decays. The overall production asymmetry in the Ds rapidity region 2.0 to 4.5 with transverse momentum larger than 2 GeV is measured to be A_P=(-0.33 +/- 0.22 +/- 0.10)%. This result can constrain models of heavy flavour production.