  High redshift quasars emit copious X-ray photons which heat the intergalactic
medium to temperatures up to $\sim$ 10$^6$ K. At such high temperatures the
primordial gas will not form stars until it is assembled into dark matter
haloes with masses of up to $\sim$ 10$^{11}$ M$_{\odot}$, at which point the
hot gas collapses and cools under the influence of gravity. Once this occurs,
there is a massive reservoir of primordial gas from which stars can form,
potentially setting the stage for the brightest Population (Pop) III starbursts
in the early Universe. Supporting this scenario, recent observations of quasars
at z $\sim$ 6 have revealed a lack of accompanying Lyman $\alpha$ emitting
galaxies, consistent with suppression of primordial star formation in haloes
with masses below $\sim$ 10$^{10}$ M$_{\odot}$. Here we model the chemical and
thermal evolution of the primordial gas as it collapses into such a massive
halo irradiated by a nearby quasar in the run-up to a massive Pop III
starburst. We find that within $\sim$ 100 kpc of the highest redshift quasars
discovered to date the Lyman-Werner flux produced in the quasar host galaxy may
be high enough to stimulate the formation of a direct collapse black hole
(DCBH). A survey with single pointings of the NIRCam instrument at individual
known high-z quasars may be a promising strategy for finding Pop III stars and
DCBHs with the James Webb Space Telescope.
