  While it is revealed that the Cosmic Microwave Background (CMB) is linearly
polarized at 10 % level, it is predicted that there exists no significant
intrinsic source for circular polarization (CP) in the standard cosmology.
However, during the propagation through a magnetised plasma, the CP of the CMB
could be produced via the Faraday conversion (FC). The FC converts a
pre-existing linear polarization into CP in presence of a magnetic field with
relativistic electrons. In this paper, we focus on the FC due to supernova
remnants of the first stars, also called Pop III stars. We derive an analytic
form for the angular power spectrum of the CP of the CMB generated by the
general FC. We apply this result to the case of the FC triggered by explosions
of the first stars and evaluate the angular power spectrum, CV V . We show that
the amplitude of l(l + 1)C_l^V V /(2pi) > 10^-2 micro Kelvin squared for l >
100, with only one Pop III star per halo, the age of Pop III SN remnants as 104
years and frequency of CMB observation as 1 GHz. We expect the CP of the CMB to
be a very promising probe of the yet unobserved first stars, primarily due to
the expected high signal along with an unique frequency dependence.
