Theoretical models predict that some of the first stars ended their lives as extremely energetic pair-instability supernovae (PISNe). With energies approaching 10⁵³ 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 rate 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 10⁴ s 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. / text