Supersymmetric neutralinos are one of the most promising candidates for the
dark matter in the Universe. If they exist, they should make up some fract
ion of the Milky Way halo. We investigate the fluxes of positrons expected
at the Earth from neutralino annihilation in the halo. Positron propagation
is treated in a diffusion model including energy loss. The positron source
function includes contributions from both continuum and monochromatic posi
trons. We find that, for a "canonical" halo model and propagation parameter
s, the fluxes are generally too low to be visible. Given the large uncertai
nties in both propagation and halo structure, it is however possible to obt
ain observable fluxes. We also investigate the shapes of the positron spect
ra, including tits to a feature indicated by the results of the HEAT experi
ment. [S0556-2821(99)00402-6].