We report the first systematic search for blazars among broad-absorption-line (BAL) quasars, by intranight
optical monitoring of a well-defined set of 10 candidates selected on the basis of a flat spectrum and an abnormally high linear polarization at radio wavelengths. A small population of BAL blazars can indeed be expected in the polar model of BAL quasars. However, no such case was found, since none of our 30 monitoring sessions devoted to the 10 candidates yielded a positive detection of intra-night optical variability (INOV). We contrast this behavior with the high duty cycle of INOV exhibited by a comparison sample of 8 normal (i.e., non-BAL) blazars and briefly explore some possible explanations.