  It was recently shown that a black hole (BH) is the only compact object that
can acquire a scalar charge in scalar Gauss-Bonnet (sGB) theory under the small
coupling approximation. This leads to the fact that scalar radiation is emitted
from a binary containing at least one BH. In this letter, we find the
constraints on this theory from BH low-mass X-ray binaries (BH-LMXBs). The main
result of this letter is that from the orbital decay rate of A0620-00, we
obtained a conservative bound that is six orders of magnitude stronger than the
solar system bound. In addition to this, we look at XTE J1118+480, whose
orbital decay rate has been recently measured with an excess compared to the
theoretical prediction in GR due to the radiation reaction. The cause of this
excess is currently unknown. Although it is likely that the cause is of
astrophysical origin, here we investigate the possibility of explaining this
excess with the additional scalar radiation in sGB theory. We find that there
still remains a parameter range where the excess can be explained while also
satisfying the constraint obtained from A0620-00. The interesting point is that
for most of other alternative theories of gravity, it seems difficult to
explain this excess with the additional radiation. This is because it would be
difficult to evade the constraints from binary pulsars or they have already
been constrained rather strongly from other observations such as solar system
experiments. We propose several ways to determine whether the excess is caused
by the scalar radiation in sGB gravity including future gravitational wave
observations with space-borne interferometers, which can give a constraint
three orders of magnitude stronger than that from A0620-00.
