  The Seebeck coefficient $S$ of the cuprate superconductor La$ _{2-x} $Sr$_{x}
$CuO$ _{4}$ (LSCO) was measured in magnetic fields large enough to access the
normal state at low temperatures, for a range of Sr concentrations from $x =
0.07$ to $x = 0.15$. For $x = 0.11$, 0.12, 0.125 and 0.13, $S/T$ decreases upon
cooling to become negative at low temperatures. The same behavior is observed
in the Hall coefficient $R_{H}(T)$. In analogy with other hole-doped cuprates
at similar hole concentrations $p$, the negative $S$ and $R_{H}$ show that the
Fermi surface of LSCO undergoes a reconstruction caused by the onset of
charge-density-wave modulations. Such modulations have indeed been detected in
LSCO by X-ray diffraction in precisely the same doping range. Our data show
that in LSCO this Fermi-surface reconstruction is confined to $0.085 < p <
0.15$. We argue that in the field-induced normal state of LSCO,
charge-density-wave order ends at a critical doping $p_{\rm CDW} = 0.15 \pm
0.005$, well below the pseudogap critical doping $p^\star \simeq 0.19$.
