  We mapped 3 mm continuum and line emission from the starburst galaxy M82
using the Combined Array for Research in Millimeter-wave Astronomy. We targeted
the HCN, HCO$^{+}$, HNC, CS and HC$_{3}$N lines, but here we focus on the HCN
and HCO$^{+}$ emission. The map covers a field of 1.2' with a ~5" resolution.
The HCN and HCO$^{+}$ observations are combined with single dish images. The
molecular gas in M82 had been previously found to be distributed in a molecular
disk, coincident with the central starburst, and a galactic scale outflow which
originates in the central starburst. With the new short spacings-corrected maps
we derive some of the properties of the dense molecular gas in the base of the
outflow. From the HCN and HCO$^{+}$ J=(1-0) line emission, and under the
assumptions of the gas being optically thin and in local thermodynamic
equilibrium, we place lower limits to the amount of dense molecular gas in the
base of the outflow. The lower limits are $7\times10^{6}$ $M_{\odot}$ and
$21\times10^{6}$ $M_{\odot}$, or $\gtrsim2\%$ of the total molecular mass in
the outflow. The kinematics and spatial distribution of the dense gas outside
the central starburst suggests that it is being expelled through chimneys.
Assuming a constant outflow velocity, the derived outflow rate of dense
molecular gas is $\geq0.3$ $M_{\odot}$ yr$^{-1}$, which would lower the
starburst lifetime by $\geq5\%$. The energy required to expel this mass of
dense gas is $(1-10)\times10^{52}$ erg.
