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Although the frustrated (zigzag) spin chain is the Drosophila of frustrated magnetism, our understanding of a pair of coupled zigzag chains (frustrated spin ladder) in a magnetic field is still lacking. We address this problem through nuclear magnetic resonance (NMR) experiments on BiCu$$_2$$${}_2$PO$$_6$$${}_6$in magnetic fields up to 45 T, revealing a field-induced spiral magnetic structure. Conjointly, we present advanced numerical calculations showing that even a 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 BiCu$$_2$$${}_2$PO$$_6$$${}_6$. An exciting possibility is that the known, DM-mediated coupling between chirality and crystal lattice may give rise to a new kind of spin-Peierls instability.