  The saturated absorption spectrum of the hyperfine-less S(0) quadrupole line
in the (2-0) band of H$_2$ is measured at $\lambda=1189$ nm, using the
NICE-OHMS technique under cryogenic conditions (72~K). It is for the first time
that a Lamb dip of a molecular quadrupole transition is recorded. At low
(150-200 W) saturation powers a single narrow Lamb dip is observed, ruling out
an underlying recoil doublet of 140 kHz. Studies of Doppler-detuned resonances
show that the red-shifted recoil component can be made visible for low
pressures and powers, and prove that the narrow Lamb dip must be interpreted as
the blue recoil component. A transition frequency of 252\,016\,361\,164\,(8)
kHz is extracted, which is off by -2.6 (1.6) MHz from molecular quantum
electrodynamical calculations therewith providing a challenge to theory.
