  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 find that a boost factor >30 provides good
fits to the HEAT data. Such an enhancement in the signal could arise if we live
in a clumpy halo.
