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We present the first high angular resolution observation of the B[e] star/X-ray transient object CI Cam, performed with the two-telescope Infrared Optical Telescope Array (IOTA), its upgraded three-telescope version (IOTA3T) and the Palomar Testbed Interferometer (PTI). Visibilities and closure phases were obtained using the IONIC-3 integrated optics beam combiner. CI Cam was observed in the near-infrared H and K spectral bands, wavelengths well suited to measure the size and study the geometry of the hot dust surrounding CI Cam. The analysis of the visibility data over an 8 yr period from soon after the 1998 outburst to 2006 shows that the dust visibility has not changed over the years. The visibility data show that CI Cam is elongated which confirms the disc-shape of the circumstellar environment and totally rules out the hypothesis of a spherical dust shell. Closure phase measurements show direct evidence of asymmetries in the circumstellar environment of CI Cam and we conclude that the dust surrounding CI Cam lies in an inhomogeneous disc seen at an angle. The near-infrared dust emission appears as an elliptical skewed Gaussian ring with a major axis , an axis ratio and a position angle . [ABSTRACT FROM AUTHOR]