  We achieve a quantum-noise-limited absorption sensitivity of
1.7/times10$^{-12}$ cm$^{-1}$ per spectral element at 400 s of acquisition time
with cavity-enhanced frequency comb spectroscopy, the highest demonstrated for
a comb-based technique. The system comprises a frequency comb locked to a
high-finesse cavity and a fast-scanning Fourier transform spectrometer with an
ultra-low-noise autobalancing detector. Spectra with a signal-to-noise ratio
above 1000 and a resolution of 380 MHz are acquired within a few seconds. The
measured absorption lineshapes are in excellent agreement with theoretical
predictions.
