This paper reports the results of the first measurements of the thermal conductivity of the \ensuremath{\alpha}, \ensuremath{\beta}, and \ensuremath{\gamma} phases of solid oxygen over the temperature range of 1--52 K. A simple qualitative analysis was performed to explain the observed anomalies in thermal conductivity, which manifested themselves by a jump at the \ensuremath{\alpha}-\ensuremath{\beta} transition, the anomalously weak temperature dependence in the \ensuremath{\beta} phase and an increase of the conductivity with temperature in the \ensuremath{\gamma} phase.