  In this paper, we solve the $L_p$ chord Minkowski problem in the case of
discrete measures whose supports are in general position for negative $p$ and
$q>0.$ As for general Borel measure with a density, we also give a proof but
need $p\in(-n,0)$ and $n+1>q\geqslant 1.$ The $L_p$ chord Minkowski problem was
recently posed by Lutwak, Xi, Yang and Zhang, which seeks to determine the
necessary and sufficient conditions for a given finite Borel measure such that
it is the $L_p$ chord measure of a convex body, and it includes the chord
Minkowski problem and the $L_p$ Minkowski problem.
