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We report the results of the first directional point-contact measurements in Mg(B_{1-x}C_{x})_2 single crystals with 0.047 <= x <= 0.132. The two-gap superconductivity typical of MgB_2 persists up to x=0.105. In this region, the values of the gaps Delta_{sigma} and Delta_{pi} were determined by fitting the Andreev-reflection conductance curves with …