We have developed a sensitive spectrometer which exploits several He-Ne laser transitions in the visible for precise, high resolution measurements of Chappuis band ozone absorption cross sections at room temperature. An overall. uncertainty of better than 1% has been achieved through a combination of transducer calibrations and an experimental procedure which unambiguously determines the impurity content of each ozone sample. The cross section near 602.5 nm is (5.16 +/- 0.03) x 10(-21) cm2/molecule. Our results compare favorably with those from most previous studies in the visible range, although some are clearly lower than this consensus probably due to errors in ozone density measurements.