Photoacoustic (PA) spectroscopic technique has become a popular tool for trace gas detection and is especially suitable for in situ measurement of sulfur hexafluoride (SF6) decomposition components in gas insulated switchgear (GIS). However, the concentrations of SF6 decomposition components are generally very low and the resulting PA signals are too weak to be accurately retrieved with traditional methods. In this study, we proposed a Lyapunov exponent based chaotic oscillator algorithm to retrieve the weak PA signals of SF6 decomposition components. Retrieval of weak PA signals from strong noise background was achieved for both simulation and measurement perspectives. The results were compared with those based on phase-locked amplification technique. Both simulation and measurement results concluded that the proposed chaotic oscillator algorithm is superior to the phase-locked amplification in terms of accuracy, sensitivity and stability. Since most trace gases have weak absorption signatures in the atmosphere (below 1%), this study can provide valuable insights in dealt with such weak signals in remote sensing of atmosphere.