  We study the effect of the supersonic relative velocity between dark matter
and baryons on large-scale galaxy clustering and derive the constraint on the
relative velocity bias parameter from the Baryonic Oscillation Spectroscopic
Survey (BOSS) power spectrum measurements. Recent work has shown that the
relative velocity effect may have a dramatic impact on the star formation at
high redshifts, if first stars are formed in minihalos around z~20, or if the
effect propagates through secondary effects to stars formed at later redshifts.
The relative velocity effect has particularly strong signatures in the large
scale clustering of these sources, including the BAO position. Assuming that a
small fraction of stars in low-redshift massive galaxies retain the memory of
the primordial relative velocity effect, galaxy clustering measurements can be
used to constrain the signatures of the first stars. Luminous red galaxies
contain some of the oldest stars in the Universe and are ideally suited to
search for this effect. Using the BOSS power spectrum measurements from the
Sloan Data Release 9, in combination with Planck, we derive the upper limit on
the fraction of the stars sensitive to relative velocity effect f_star<3.3% at
the 95% confidence level in the CMASS galaxy sample. If additional galaxy
sample not sensitive to the effect is available in a given survey, a joint
multi-tracer analysis can be applied to construct a sample-variance cancelling
combination, providing a model-independent way to verify the presence of the
relative velocity effect in the galaxy power spectrum on large scales. Such a
multi-tracer analysis in future galaxy surveys can greatly improve the current
constraint, achieving a 0.1% level in f_star.
