  Chord measures and $L_p$ chord measures were recently introduced by
Lutwak-Xi-Yang-Zhang by establishing a variational formula regarding a family
of fundamental integral geometric invariants called chord integrals.
Prescribing the $L_p$ chord measure is known as the $L_p$ chord Minkowski
problem, which includes the $L_p$ Minkowski problem heavily studied in the past
2 decades as special cases. In the current work, we solve the $L_p$ chord
Minkowski problem when $0\leq p<1$, without symmetry assumptions.
