A search for the doubly charmed baryon Xi_cc^+ in the decay mode Xi_cc^+ -> Lambda_c^+ K^- pi^+ is performed with a data sample, corresponding to an integrated luminosity of 0.65/fb, of pp collisions recorded at a centre-of-mass energy of 7 TeV. No significant signal is found in the mass range 3300-3800 MeV/c^2. Upper limits at the 95% confidence level on the ratio of the Xi_cc^+ production cross-section times branching fraction to that of the Lambda_c^+, R, are given as a function of the Xi_cc^+ mass and lifetime. The largest upper limits range from R < 1.5 x 10^-2 for a lifetime of 100 fs to R < 3.9 x 10^-4 for a lifetime of 400 fs.
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