  The existence of $^{12}{\rm C} + {}^{16}{\rm O}$ molecular resonances at
sub-barrier energy has been a significant problem in nuclear astrophysics
because they strongly affect the $^{12}{\rm C} + {}^{16}{\rm O}$ fusion
reaction rate in type Ia supernovae and heavy stars. However, experimental
surveys have been limited to 4~MeV and cannot access the deep sub-barrier
energy due to a very small fusion cross section. Here we predict a couple of
resonances with $J^\pi=0^+$, $2^+$, and $4^+$ in the deep sub-barrier energy
based on the antisymmetrized molecular dynamics calculation that reproduces the
known resonances and low-lying spectrum of $^{28}{\rm Si}$.
