There is strong evidence that magnetic interactions play a crucial role in the mechanism driving high-temperature superconductivity in cuprate superconductors. To investigate this further we have done neutron scattering experiments on the simplest high-temperature superconductor La(2-x)Sr(x)CuO(4) (LSCO) in an applied magnetic field. Below the superconducting transition temperature (Tc), the field penetrates the material via an array of normal state inclusions or vortices while phase coherent superconductivity characterized by zero resistance is suppressed to the lower field-dependent irreversibility temperature. The measurements described here were performed on underdoped LSCO (x=0.10), which develops static incommensurate order below Tc in zero field. Our results show that application of a magnetic field enhances this response without changing the onset temperature. For H=5T the field-induced signal saturates to three times the zero-field signal and phase coherent superconductivity is established within the antiferromagnetic phase.