Denitrification is the biological reduction of nitrate \((NO_3^-)\) to nitrogen gas \((N_2)\) by facultative anaerobic bacteria.
It occurs under anoxic conditions where oxygen is absent and organic carbon serves as the electron donor.
Hence,
\[
\boxed{\text{Anoxic conditions with organic carbon}}
\]
is the correct answer.
Therefore,
\[
\boxed{(C)}
\]