The accurate determination of transport properties near the critical points is of great current interest. We present here new data of 0.3% accuracy for the thermoelectric power S of chromium below the Néel temperature TN which was obtained with a temperature difference of only 0.5 K. Extensive computer fitting to diverse theoretically predicted forms for S(T) does not yield an unambiguous critical exponent, nor does it let us make distinction between different forms. These ambiguities arise from our ignorance of the functional form of the normal background of S and the lack of precise knowledge of TN. The latter is due to the fact that the transition is of first order, and, it can be argued, it masks a second-order transition occurring at a higher temperature if one approaches TN from below. This higher temperature would then be the appropriate temperature for the analysis of fluctuation effects.