  Constraining the properties of Population III (Pop III) stars will be very
challenging because they reside in small galaxies at high redshift which will
be difficult to directly detect. In this paper, we suggest that intensity
mapping may be a promising method to study Pop III stars. Intensity mapping is
a technique proposed to measure large-scale fluctuations of galaxy line
emission in three dimensions without resolving individual sources. This
technique is well suited for observing many faint galaxies because it can
measure their cumulative emission even if they cannot be directly detected. We
focus on intensity mapping of He II recombination lines. These lines are much
stronger in Pop III stars than Pop II stars because the harder spectra of Pop
III stars are expected to produce many He II ionizing photons. Measuring the He
II 1640 \AA{} intensity mapping signal, along with the signals from other lines
such as Ly$\alpha$, H$\alpha$, and metal lines, could give constraints on the
initial mass function (IMF) and star formation rate density (SFRD) of Pop III
stars as a function of redshift. To demonstrate the feasibility of these
observations, we estimate the strength of the Pop III He II 1640 \AA{}
intensity mapping signal from $z=10-20$. We show that at $z\approx10$, the
signal could be measured accurately by two different hypothetical future
instruments, one which cross-correlates He II 1640 \AA{} with CO(1-0) line
emission from galaxies and the other with 21 cm emission from the intergalactic
medium (IGM).
