  At redshift z>5 Type II supernovae (SNII) are the only known dust sources
with evolutionary timescales shorter than the Hubble time. We extend the model
of dust formation in the ejecta of SNII by Todini & Ferrara (2001) to
investigate the same process in pair-instability supernovae (PISN), which are
though to arise from the explosion of the first, metal free, very massive
(140-260 Msun) cosmic stars. We find that 15%-30% of the PISN progenitor mass
is converted into dust, a value >10 times higher than for SNII; PISN dust
depletion factors (fraction of produced metals locked into dust grains) range
between 0.3 and 0.7. These conclusions depend very weakly on the mass of the
PISN stellar progenitor, which instead affects considerably the composition and
size distribution. For the assumed temperature evolution, grain condensation
starts 150-200 days after the explosion; the dominant compounds for all
progenitor masses are SiO2 and Mg2SiO4 while the contribution of amorphous
carbon and magnetite grains grows with progenitor mass; typical grain sizes
range between 0.001 and a few 0.1 micron and are always smaller than 1 micron.
We give a brief discussion of the implications of dust formation for the IMF
evolution of the first stars, cosmic reionization and the intergalactic medium.
