We propose a supersymmetric explanation for the anomalously high forward backward asymmetry in top pair production measured by CDF and D0. We suppose that it is due to the t-channel exchange of a right-handed sbottom which couples to d_R and t_R, as is present in the R-parity violating minimal supersymmetric standard model. We show that all Tevatron and LHC experiments t tbar constraints may be respected for a sbottom mass between 300 and 1200 GeV, and a large Yukawa coupling >2.2, yielding A_{FB} up to 0.18. The non Standard Model contribution to the LHC charge asymmetry parameter is Delta A_C^y=0.017-0.045, small enough to be consistent with current measurements but non-zero and positive, allowing for LHC confirmation in the future within 20 fb^-1. A small additional contribution to the LHC t tbar production cross-section is also predicted, allowing a further test. We estimate that 10 fb^-1 of LHC luminosity would be sufficient to rule out the proposal to 95% confidence level, if the measurements of the t tbar cross-section turn out to be centred on the Standard Model prediction.
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