  We demonstrate a possibility to stabilize three-dimensional spatiotemporal
solitons ("light bullets") in self--focusing Kerr media by means of a
combination of dispersion management in the longitudinal direction (with the
group-velocity dispersion alternating between positive and negative values) and
periodic modulation of the refractive index in one transverse direction, out of
the two. The analysis is based on the variational approximation (results of
direct three-dimensional simulations will be reported in a follow-up work). A
predicted stability area is identified in the model's parameter space. It
features a minimum of the necessary strength of the transverse modulation of
the refractive index, and finite minimum and maximum values of the soliton's
energy. The former feature is also explained analytically.
