  Theoretical models predict that some of the first stars ended their lives as
extremely energetic pair-instability supernovae (PISNe). With energies
approaching 10^53 ergs, these supernovae are expected to be within the
detection limits of the upcoming James Webb Space telescope (JWST), allowing
observational constraints to be placed on the properties of the first stars. We
estimate the source density of PISNe using a semi-analytic halo mass function
based approach, accounting for the effects of feedback from star formation on
the PISN rates using cosmological simulations. We estimate an upper limit of
~0.2 PISNe per JWST field of view at any given time. Feedback can reduce this
rate significantly, e.g., lowering it to as little as one PISN per 4000 JWST
fields of view for the most pessimistic explosion models. We also find that the
main obstacle to observing PISNe from the first stars is their scarcity, not
their faintness; exposures longer than a few times 10^4s will do little to
increase the number of PISNe found. Given this we suggest a mosaic style search
strategy for detecting PISNe from the first stars. Even rather high redshift
PISNe are unlikely to be missed by moderate exposures, and a large number of
pointings will be required to ensure a detection.
