  Although the frustrated spin chain (zigzag chain) is a Drosophila of
frustrated magnetism, the understanding of a pair of coupled zigzag chains
(frustrated spin ladder) in a magnetic field is incomplete. We address this
problem through nuclear magnetic resonance (NMR) experiments on
$\text{BiCu}_2\text{PO}_6$ in magnetic fields up to 45 T, revealing a
field-induced spiral magnetic structure. Conjointly, we present advanced
numerical calculations showing that even moderate rung coupling dramatically
simplifies the phase diagram below half-saturation magnetization by stabilizing
a field-induced chiral phase. Surprisingly for a one-dimensional model, this
phase and its response to Dzyaloshinskii-Moriya (DM) interactions adhere to
classical expectations. While explaining the behavior at the highest accessible
magnetic fields, our results imply a different origin for the solitonic phases
occurring at lower fields in $\text{BiCu}_2\text{PO}_6$. An exciting
possibility is that the known, DM-mediated coupling between chirality and
crystal lattice gives rise to a new kind of spin-Peierls instability.
