  We propose an experimentally relevant scheme to create stable solitons in a
three-dimensional Bose-Einstein condensate confined by a one-dimensional
optical lattice, using temporal modulation of the scattering length (through ac
magnetic field tuned close to the Feshbach resonance). Another physical
interpretation is a possibility to create stable 3D "light bullets" in an
optical medium with a longitudinal alternating self-focusing/defocusing
structure, and periodic modulation of the refractive index in a transverse
direction. We develop a variational approximation to identify a stability
region in the parametric space, and verify the existence of stable breathing
solitons in direct simulations. Both methods reveal that stable solitons may be
supported if the average value of the nonlinear coefficient (whose sign
corresponds to attraction between atoms) and the lattice's strength exceed
well-defined minimum values. Stable localized patterns may feature a multi-cell
structure.
