Positron annihilation lifetime spectroscopy (PALS) measurements were performed on a series of syndiotactic polystyrene (s-PS) samples crystallized from the melt state. These s-PS samples contained either pure alpha or beta forms with various crystallinities. The alpha and beta crystalline forms are known to have densities very similar to the amorphous phase. The low-density is believed to be associated with nanovoids or nanochannels, existing between the polymer chains in crystalline s-PS. A question can be raised whether positronium can form and annihilate in these low-density crystalline structures. In analyzing the PALS spectra, it was found that four distinct lifetime components gave the best fit for all studied samples. The longest lifetime component (tau(4) = 2-3 ns) exhibits thermal expansion behavior typical of amorphous polymers, while the second longest lifetime (tau(3) similar to 0.8 ns) is constant, independent of temperature, crystallinity and tacticity. For all sernicrystalline and amorphous s-PS samples, the PALS spectra were found to be essentially indistinguishable, with remarkably similar lifetimes and intensities. This behavior implies that ortho-positronium can indeed form in the low-density crystal structures of s-PS. Two possibilities for ortho-positronium annihilation in the semicrystalline polymer were proposed and analyzed: (a) ortho-positronium annihilates in the crystal phase with a lifetime characteristic of the nanochannel dimensions; (b) ortho-positronium rapidly diffuses into the amorphous phase and annihilates with a lifetime typical of that phase. No evidence for the existence of a lifetime component characteristic of the crystal nanochannels was found, indicating that the second annihilation mechanism is dominant.