Progenitors of long gamma-ray bursts (GRBs), and of core-collapse supernovae in general, may have two separate mechanisms driving the outflows: quasi-isotropic neutrino-driven supernova explosions followed by a highly collimated relativistic outflow driven by the GRB central engine, a black hole or a magnetar. We consider the dynamics of the second GRB-driven explosion propagating through the expanding envelope generated by the passage of the primary supernova shock. Beyond the central core, in the region of steep density gradient created by the supernova shock breakout, the accelerating secondary quasi-spherical GRB shock becomes unstable to corrugation and under certain conditions may form a highly collimated jet, a ‘chimney’, when a flow expands almost exclusively along a nearly cylindrically collimated channel. Thus, weakly non-spherical driving and/or non-spherical initial conditions of the wind cavity may produce highly non-spherical, jetted outflows. For a constant luminosity GRB central engine, this occurs for density gradient in the envelope ρ∝r−ω steeper than ω > 4.