Neutron scattering is used to study magnetic field induced ordering in the quasi-1D quantum spin-tube compound Sul--Cu$_2$Cl$_4$ that in zero field has a non-magnetic spin-liquid ground state. The experiments reveal an incommensurate chiral high-field phase stabilized by a geometric frustration of the magnetic interactions. The measured critical exponents $betaapprox0.235$ and $ uapprox0.34$ at $H_capprox3.7$ T point to an unusual sub-critical scaling regime and may reflect the chiral nature of the quantum critical point.
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