Cosmic ray positron excess and neutralino dark matter

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 >~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.