Comet C/1995 O1 Hale-Bopp was observed with the adaptive optics system ADONIS on the ESO 3.6 m telescope at La Silla, Chile, through the broadband J, H, K, SK (Short K) filters on 6 November 1997 and 15 January 1998. After processing of the images using different restoration techniques, the maximum brightness in the coma appeared as a double peak. The separation between the two components was 0.23 " in November 1997 and 0.36 " in January 1998. Furthermore, broad jet features were traced in our images of the inner coma. While lightshift effects could be excluded, dust knots in near-nucleus jets could explain the observed double peak. Nevertheless, an attractive scenario is that the comet actually has a double nucleus, which could even be gravitationally bound. The presence of jets with opposite curvatures, as observed in Hale-Bopp's coma on 22 January 1998 at optical wavelengths, provides additional support for the binary-nucleus interpretation. Indeed such features are difficult to explain by a single rotating nucleus, but they would be easily understood if two nuclei were involved. The pros and cons of the interpretations are discussed, but no final conclusion on the validity of either of them is possible on the basis of the observations available to our group.