Low-dimensional magnets with low-spin quantum number are ideal model systems for investigating strongly interacting macroscopic quantum ground states and their non-linear spin excitations. We present single-crystal neutron-diffraction measurements of the ordered phase of the quasi-one-dimensional spin-1/2 XY antiferromagnet Cs2CoCl4 both in zero field and in fields up to 6.5 T. In zero field the system shows long-range order below TN=217 mK with a commensurate ordering wave-vector (0,0.5,0.5). With increasing magnetic field – applied perpendicular to the magnetic chain axis – the magnetic Bragg peak intensities increase monotonically, reaching a maximum at H=1.4 T; evidence that the magnetic field suppresses quantum fluctuations in the ground state. At Hc=2.1 T the ordered structure collapses in an apparent first-order phase transition, with no magnetic Bragg peaks being observed in the (0,k,l) scattering plane above this field. This result suggests that the magnetic field induces a phase transition to a spin-liquid ground state. Magnetic Bragg peak intensities at ferromagnetic positions increase quadratically up to about 2.8 T, corresponding to a linear increase of the magnetic moment. At higher magnetic fields, the intensity increases linearly up to 6.5 T.