  We propose a new hypothesis for the origin of non-solar hadronic cosmic rays
(CRs) at all energies: Highly relativistic, narrowly collimated jets from the
birth or collapse of neutron stars (NSs) in our Galaxy accelerate ambient disk
and halo matter to CR energies and disperse it in ``hot spots'' which they form
when they stop in the Galactic halo. Such events - ``Galactic Gamma-Ray
Bursters'' (GGRBs) - are proposed to cause cosmological gamma-ray bursts (GRBs)
in other galaxies when their beamed radiation happens to point in our
direction. Our hypothesis naturally explains some observations which are
difficult to understand with the currently popular ideas about CR origin - e.g.
the small Galacto-centric gradient of the cosmic-ray density and the absence of
the Greisen-Zatsepin-Kuzmin cutoff. Our idea stands or falls with the existence
of the ``hot spots'' (``GGRB remnants'') in the Galactic halo. We discuss their
expected observational signatures and find that they could appear as EGRET
unidentified high-latitude sources.
