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We present HI imaging of GBT 1355+5439 performed with the Westerbork Synthesis Radio Telescope. This is a dark HI object recently discovered close to the nearby galaxy M101. We find GBT 1355+5439 to be an HI cloud 5x3 arcmin in size. The total HI image and the kinematics show that the cloud consists of condensations that have small (~10 km/s) motions with respect to each other. The column densities of the HI are low; the observed peak value is 7.1x10^{19} cm^{-2}. The velocity field shows a mild velocity gradient over the body of GBT 1355+5439, possibly due to rotation, but it may also indicate large-scale radial motions. Although our data are limited in sensitivity, at all positions the HI velocity dispersion is higher than 5 km/s and no narrow, cold, HI component is seen. Because its distance is not known, we considered various possibilities for the nature of GBT 1355+5439. Both the scenarios that it is a tidal remnant near M101 and that it is a dark dwarf companion of M101 meet difficulties. Neither do the data fit the properties of known compact High-Velocity Clouds in the Galactic halo exactly, but we cannot entirely exclude this option and deeper observations are required. We also considered the possibility that GBT 1355+5439 is a gas-rich dark minihalo in the outer regions of the Local Group. Interestingly, it would then have similar properties as the clouds of a proposed Local Group population recently found in the ALFALFA survey. In this case, the HI mass of GBT 1355+5439 would be about a few times 10^5 Msol, its size about 1 kpc, and the dynamical mass M_dyn > 5x10^7 Msol. However, if GBT 1355+5439 is a dark Local Group object, the internal kinematics of the HI appears to be different from that of gas-dominated, almost dark galaxies of similar size.
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