  Emergence of odd-frequency s-wave superconductivity is demonstrated in the
two-channel Kondo lattice by means of the dynamical mean-field theory combined
with the continuous-time quantum Monte Carlo method. Around half filling of the
conduction bands, divergence of an odd-frequency pairing susceptibility is
found, which signals instability toward the superconductivity. The
corresponding order parameter is equivalent to a staggered composite-pair
amplitude with even frequencies, which involves both localized spins and
conduction electrons. A model wave function is constructed for the composite
order with use of symmetry operations such as charge conjugation and channel
rotations. Given a certain asymmetry of the conduction bands, another s-wave
superconductivity is found that has a uniform order parameter. The Kondo effect
in the presence of two channels is essential for both types of unconventional
superconductivity.
