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 \farcm { } 2 with a { \approx 5 \arcsec } 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 ^ { + } { \mbox { 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 \times 10 ^ { 6 } } M _ { \odot } and { 21 \times 10 ^ { 6 } } M _ { \odot } , or \gtrsim 2 \% 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 { \geq 0.3 } M _ { \odot } yr ^ { -1 } , which would lower the starburst lifetime by \geq 5 \% . The energy required to expel this mass of dense gas is { ( 1 - 10 ) \times 10 ^ { 52 } } erg .