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Dark Matter (DM) can be trapped by the gravitational field of any star, since collisions with nuclei in dense environments can slow down the DM particle below the escape velocity ($v_{esc}$) at the surface of the star. If captured, the DM particles can self-annihilate, and, therefore, provide a new source of energy for the star. We investigate this phenomenon for capture of DM particles by the first generation of stars [Population III (Pop III) stars], by using the multiscatter capture formalism. Pop III stars are particularly good DM captors, since they form in DM-rich environments, at the center of$~\sim 10^6 M_\odot$ DM minihalos, at redshifts $z\sim 15$. Assuming a DM-proton scattering cross section ($σ)$ at the current deepest exclusion limits provided by the XENON1T experiment, we find that captured DM annihilations at the core of Pop III stars can lead, via the Eddington limit, to upper bounds in stellar masses that can be as low as a few $M_\odot$ if the ambient DM density ($ρ_X$) at the location of the Pop III star is sufficiently high. Conversely, when Pop III stars are identified, one can use their observed mass ($M_\star$) to place bounds on $ρ_Xσ$. Using adiabatic contraction to estimate the ambient DM density in the environment surrounding Pop III stars, we place projected upper limits on $σ$, for $M_\star$ in the $100-1000~M_\odot$ range, and find bounds that are competitive with, or deeper than, those provided by the most sensitive current direct detection experiments for both spin independent and spin dependent interactions, for a wide range of DM masses. Most intriguingly, we find that Pop III stars with mass $M_\star \gtrsim 300 M_\odot$ could be used to probe the SD proton-DM cross section below the "neutrino floor," i.e. the region of parameter space where DM direct detection experiments will soon become overwhelmed by neutrino backgrounds.