Population III stars formed just a few hundred million years after the Big Bang, out of hydrogen and helium made in primordial nucleosynthesis. Theory predicts that such Population III stars were typically very massive, different from the present-day Milky Way Galaxy, which is dominated by low-mass stars like our Sun. Because of their high mass, the first stars are predicted to be very luminous, but also very short-lived. One of the key challenges in observational astronomy is to detect Population III stars, so that we can constrain our emerging theoretical picture. Despite their intrinsic brightness, even the most powerful telescopes currently in operation cannot yet directly observe the first stars, because of their extreme distance. We thus need to focus on the remnants left behind when Population III stars die. Such black hole or neutron star remnants can act as indirect probes of the early universe, and a number of them are expected to survive throughout cosmic history, so that we can search for them in our immediate cosmic neighborhood. Neutron star remnants from Population III have not been studied yet, as black hole remnants are more researched. We set out to investigate these neutron star remnants in order to assess the feasibility of detecting a Population III remnant in our Milky Way. First, we use the Press-Schechter analytical formalism to calculate the number of dark matter minihalos, regions where Population III stars form, that are incorporated into the present-day Milky Way. Then, we determine the amount of star forming gas available per minihalo, combined with the initial mass function of Population III stars, to find the number of neutron star remnants per minihalo. From this, we are able to discern that there are about 20,000 Population III neutron star remnants in the Milky Way. Next we seek to distinguish these remnants from those of Population I and II stars. Since they are expected to be more massive, it stands to reason that they are also brighter. We calculate a timescale for binary capture of 106 years, implying that a Population III neutron star will acquire a companion every million years. Due to the bright accretion-powered emission from such binaries, we should be able to detect these sources. We are constructing a luminosity function that will show the number of neutron stars at a particular luminosity as a function of Eddington luminosity. At the high-luminosity end of this plot, we expect to find the signature of Population III remnants. From this, we can constrain the properties of the first stars, thus guiding direct searches with next-generation telescopes, such as the James Webb Space Telescope.