The primordial anisotropies of the cosmic microwave background (CMB) are linearly polarized via Compton-scattering. The Faraday conversion process during the propagation of polarized CMB photons through regions of the large-scale structure containing magnetized relativistic plasma, such as galaxy clusters, will lead to a circularly polarized contribution. Though the resulting Stokes-V parameter is of order 10 −9 at frequencies of 10 GHz, the contribution can potentially reach the level of total Stokes-U at low frequencies due to the cubic dependence on the wavelength. In future, the detection of circular polarization of CMB can be used as a potential probe of the physical properties associated with relativistic particle populations in large-scale structures.The CMB anisotropies are expected to be linearly polarized by anisotropic Compton scattering around the epoch of recombination [1]. This linear polarization field has been widely discussed in the literature [2] and its accurate measurement can ultimately shed new light on the thermal history of the universe and on the primordial gravitational-wave background. It is also well established that, in the standard scenario, no relevant circular polarization should be present. For these reasons, many of the present and near future CMB experiments like MAP and Planck Surveyor have not been designed for a detection of circular polarization.It is therefore quite probable that in the near future, in spite of a continuous incremental knowledge on linear CMB polarization, the experimental bounds on the circular component will not drastically improve from those of early observations [3]. Since post-Planck CMB polarization experiments are already under study [4], it is extremely timely to address the question whether CMB is circularly polarized and what physical information can be extracted from its measurement. This letter represents a discussion in this direction.In order to understand the CMB polarization field, we make use of the Stokes parameters [5]. In the case of a propagating wave in the z direction, E = (E x e iφxx + E y e iφyŷ )e −iωt , with amplitudes E x and E y in the x and y-directions with phases φ x and φ y , respectively, we can write the Stokes parameters as time averaged quantities:Note that the total intensity of the radiation is given by the Stokes-I parameter, while for unpolarized radiation Q = U = V = 0. The linearly polarized radiation is defined by non-zero values for Q and/or U . These latter two Stokes parameters form a spin-2 basis; A rotation of the coordinate system, by an angle θ, leads to a new set of parameters for the same radiation field given by (Q ± iŪ) = (Q ± iU )e 2iθ . This coordinate dependence is avoided in the literature by introducing a new set of orthonormal basis with a part containing the gradient of a scalar field, called grad-or E-modes, and a part containing the curl of a vector field, called curl-or Bmodes [6]. Note that the Stokes-V parameter, which is coordinate-independent similar to Stokes-I, defines the extent to whi...