  In the collapsar scenario of the long duration Gamma-Ray Bursts (GRBs),
multi-TeV neutrino emission is predicted as the jet makes its way through the
stellar envelope. Such a neutrino signal is also expected for more general
``failed'' GRBs in which a putative jet is ``choked'' by a heavy envelope. If
the \nu_e \rightarrow \nu_\mu neutrino oscillation parameters are in the
atmospheric neutrino oscillation range, we show that the resonant oscillation
of \nu_e\leftrightarrow\nu_{\mu,\tau} can take place within the inner high
density region of the choked jet progenitor with a heavy envelope, altering the
neutrino flavor ratio on its surface to
\Phi^s_{\nu_e}:\Phi^s_{\nu_\mu}:\Phi^s_{\nu_\tau}=5:11:2. Considering vacuum
oscillation of these neutrinos on their way to Earth, the final flavor ratio
detected on Earth is further modified to either $1:1.095:1.095$ for the large
mixing angle solution to the solar neutrino data, or 1:1.3:1.3 for maximal
mixing among the muon and tau neutrinos in vacuum.
