  We present the 3-point function \xi_3 and Q_3=\xi_3/\xi_2^2 for a
spectroscopic sample of luminous red galaxies (LRG) from SDSS DR6 & DR7. We
find a strong (S/N$>$6) detection of $Q_3$ on scales of 55-125 Mpc/h, with a
well defined peak around 105 Mpc/h in all \xi_2, \xi_3 and Q_3, in excellent
agreement with the predicted shape and location of the imprint of the baryon
acoustic oscillations (BAO). We use very large simulations to asses and test
the significance of our measurement. Models without the BAO peak are ruled out
by the $Q_3$ data with 99% confidence. Our measurements show the expected shape
for Q_3 as a function of the triangular configuration. This provides a first
direct measurement of the non-linear mode coupling coefficients of density and
velocity fluctuations which, on these large scales, are independent of cosmic
time, the amplitude of fluctuations or cosmological parameters. The location of
the BAO peak in the data indicates \Omega_m =0.28 \pm 0.05 and \Omega_B=0.079
\pm 0.025 (h=0.70) after marginalization over spectral index (n_s=0.8-1.2)
linear b_1 and quadratic c_2 bias,which are found to be in the range:
b_1=1.7-2.2 and c_2=0.75-3.55. The data allows a hierarchical contribution from
primordial non-Gaussianities in the range Q_3=0.55-3.35. These constraints are
independent and complementary to the ones that can be obtained using the
2-point function, which are presented in a separate paper. This is the first
detection of the shape of $Q_3$ on BAO scales, but our errors are shot-noise
dominated and the SDSS volume is still relatively small, so there is ample room
for future improvement in this type of measurements.
