The magnetic phase diagram of the Cr100− zOs z alloy system exhibits possible quantum critical behavior (QCB), with commensurate spin-density-wave to paramagnetic (CSDW-PM) phase line terminating at z ≈ 14, in a superconducting dome at z ≈ 12. Also indicated is the co-existence of SDW antiferromagnetism (AFM) and superconductivity (SC) for the z = 12.2 sample with a bcc structure. Considering the unique behaviour in the Cr100− zOs z system, this study reports on an investigation into the temperature dependence of the thermoelectric power or Seebeck coefficient, [Formula: see text]. With S( T) sensitive to the electronic structure and scattering mechanisms it is used here in order to investigate the unique magnetic behaviour observed in this alloy. [Formula: see text] measurements were performed on polycrystalline Cr100− zOs z (2.1 ≤ z ≤ 14.1) samples, as confirmed by XRD to be in a single bcc phase. The low-temperature S( T) behaviour is expressed in the form S = aT + bT3, where a and b are constants that were determined to discuss the possible contributions of phonon and/or magnon drag to S. Resulting a( z) and b( z) behaviour indicate anomalies that can be associated with three crucial points in the Cr100− zOs z magnetic phase diagram: (i) at z ≈ 8 is associated with the destabilization of the CSDW phase with the continual addition of Os into the system, (ii) at z ≈ 12 where the SC properties manifest and (iii) at z ≈ 13 associated with quantum critical behaviour this the system. Considering d S/d T where T approaches 0 K, as function of z, clear anomalies are observed at z ≈ 12 and 13, which, are associated with the onset of SC and QCB in this system. The present results suggest that S is a decisive experimental parameter in characterizing anomalous behaviour reflected in the magnetic phase diagram of Cr100− zOs z.