  Using a new instrument, the HEAT collaboration has confirmed the excess of
cosmic ray positrons that they first detected in 1994. We explore the
possibility that this excess is due to the annihilation of neutralino dark
matter in the galactic halo. We confirm that neutralino annihilation can
produce enough positrons to make up the measured excess only if there is an
additional enhancement to the signal. We quantify the `boost factor' that is
required in the signal for various models in the Minimal Supersymmetric
Standard Model parameter space, and study the dependence on various parameters.
We find models with a boost factor greater than 30. Such an enhancement in the
signal could arise if we live in a clumpy halo. We discuss what part of
supersymmetric parameter space is favored (in that it gives the largest
positron signal), and the consequences for other direct and indirect searches
of supersymmetric dark matter.
