  We present observations of NGC 4038/39 in the [CII] 158 micron fine structure
line taken with the MPE/UCB Far-infrared Imaging Fabry-Perot Interferometer
(FIFI) on the KAO with 55" resolution. The total [CII] luminosity of the
Antennae is 3.7x10^8 L(sun), which is about 1% of the FIR luminosity. The main
part of the [CII] emission probably arises from photodissociation regions
(PDRs). Up to 1/3 of the observed [CII] emission may originate from the CNM for
higher temperatures and densities. From PDR models we derive densities and FUV
intensities for the nuclei and the interaction zone. The minimum masses in the
[CII] emitting regions in the interaction zone and the nuclei are a few x
10^(7) M(sun). We find that the [CII] to CO intensity ratio at the interaction
zone is a factor of 2.6 lower than usually observed in starburst galaxies, but
still a factor of about 1.3 to 1.4 higher than at the nuclei of NGC 4038/39,
indicating no global starburst is taking place in the Antennae. [CII] emission
arising partly from confined starburst regions and partly from surrounding
quiescent clouds could explain the observed [CII] radiation at the interaction
zone and the nuclei. There are small confined regions with high star formation
activity in the interaction zone and with a lower star formation activity in
the nuclei. This supports the high density and high FUV intensity for the PDRs
in the interaction zone and the nuclei.
