  High redshift, massive halos are observed to have sustained, high star
formation rates, which require that the amount of cold gas in the halo is
continuously replenished. The cooling time scale for the hot virialized halo
gas is too long to provide the source of cold gas. Supersonic, cold streams
have been invoked as a mechanism for feeding massive halos at high redshift and
deliver the cold gas required for continued star formation at the rates
observed. This mechanism for replenishing the cold gas reservoir is motivated
by some cosmological simulations. However, the cold streams are likely to be
subject to the supersonic version of the Kelvin-Helmholtz instability (KHI),
which eventually leads to stream disruption. Cosmological simulations have yet
to obtain the spatial resolution required for understanding the detailed
stability properties of cold streams. In this paper, we consider instead an
idealized model of magnetized cold streams that we spatially resolve. Using
linear theory we show how magnetic fields with dynamically important field
strengths do not inhibit the KHI but rather enhance its growth rate. We perform
nonlinear simulations of magnetized stream disruption and find that magnetic
fields can nevertheless increase stream survival times by suppressing the
mixing rate of cold gas with the circumgalactic medium. We find that magnetic
fields can allow streams to survive $\sim 2-8$ times longer and, consequently,
that streams $\sim 2-8$ times thinner can reach the central galaxy if the
magnetic field strength is $\sim 0.3-0.8 \mu$G.
