Ice I exhibits a complex rheology at temperature and pressure conditions appropriate for the interiors of the ice I shells of Europa, Ganymede, and Callisto. We use numerical methods and existing parameterizations of the critical Rayleigh number to determine the conditions required to trigger convection in an ice I shell with each of the stress-, temperature- and grain size--dependent rheologies measured in laboratory experiments by Goldsby and Kohlstedt (2001). The critical Rayleigh number depends on the ice grain size and the amplitude and wavelength of temperature perturbation issued to an initially conductive ice I shell. If the shells have an assumed uniform grain size <0.4 mm, deformation during initial plume growth is accommodated by Newtonian volume diffusion. If the ice grain size is between 0.4 mm and 3 cm, deformation during plume growth is accommodated by weakly non-Newtonian grain boundary sliding, where the critical ice shell thickness for convection depends on the amplitude of temperature perturbation to the -0.5 power. If the ice grain size exceeds 2 cm, convection can not occur in the ice I shells of the Galilean satellites regardless of the amplitude or wavelength of temperature perturbation. If the grain size in a convecting ice I shell evolves to effective values greater than 2 cm, convection will cease. If the ice shell has a grain size large enough to permit flow by dislocation creep, the ice is too stiff to permit convection, even in the thickest possible ice I shell. Consideration of the complex ice rheology implies that estimates of the grain size in the satellites and knowledge of their initial thermal states are required when judging the convective instability of their ice I shells.