  With the MIPS camera on Spitzer, we have searched for far-infrared emission
from dust in the planetary system orbiting pulsar PSR 1257+12. With accuracies
of 0.05 mJy at 24 um and 1.5 mJy at 70 um, photometric measurements find no
evidence for emission at these wavelengths. These observations place new upper
limits on the luminosity of dust with temperatures between 20 and 1000 K. They
are particularly sensitive to dust temperatures of 100-200 K, for which they
limit the dust luminosity to below $3 \times 10^{-5}$ of the pulsar's spin-down
luminosity, three orders of magnitude better than previous limits. Despite
these improved constraints on dust emission, an asteroid belt similar to the
Solar System's cannot be ruled out.
