Many extensions of the Standard Model involve two Higgs doublet fields to break the electroweak symmetry, leading to the existence of three neutral and two charged Higgs particles. In particular, this is the case of the Minimal Supersymmetric extension of the Standard Model, the MSSM. A very important parameter is tanβ defined as the ratio of the vacuum expectation value of the two Higgs doublets. In this Letter we focus on the left–right asymmetry in the production of polarised top quarks in association with charged Higgs bosons at the LHC. This quantity allows for a theoretically clean determination of tanβ. In the MSSM, the asymmetry remains sensitive to the strong and electroweak radiative corrections and, thus, to the superparticle spectrum. Some possible implications of these results are discussed.