  Some of the first stars could be cooler and more massive than standard
stellar models would suggest, due to the effects of dark matter annihilation in
their cores. It has recently been argued that such objects may attain masses in
the 10^4--10^7 solar mass range, and that such supermassive dark stars should
be within reach of the upcoming James Webb Space Telescope. Notwithstanding
theoretical difficulties with this proposal, we argue here that some of these
objects should also be readily detectable with both the Hubble Space Telescope
and ground-based 8--10 m class telescopes. Existing survey data already place
strong constraints on 10^7 solar mass dark stars at z~10. We show that such
objects must be exceedingly rare or short-lived to have avoided detection.
