Field-induced antiferromagnetic (AF) fluctuations and magnetization are observed above the (zero-field) ordering temperature, TN = 23 K by electron spin resonance in κ-(BEDT-TTF)2Cu[N(CN)2]Cl, a quasi two-dimensional antiferromagnet with a large isotropic Heisenberg exchange interaction. The Dzyaloshinskii-Moriya (DM) interaction is the main source of anisotropy, the exchange anisotropy and the interlayer coupling are very weak. The AF magnetization is induced by magnetic fields perpendicular to the DM vector; parallel fields have no effect. The different orientation of the DM vectors and the g factor tensors in adjacent layers allows the distinction between interlayer and intralayer correlations. Magnetic fields induce the AF magnetization independently in adjacent layers. We suggest that the phase transition temperature, TN is determined by intralayer interactions alone.PACS numbers: 76.30.-v, 76.50+g, 75.30-m One-dimensional (1D) magnets, i.e., isolated chains of magnetic atoms or molecules have no ordering phase transitions while 3D magnets order at finite temperatures, T N . Magnetic ordering in two dimensions, i.e., in isolated planes, is a delicate question [1]. Theory predicts for most anisotropic two-dimensional (2D) magnets a phase transition at finite T N except if ordering breaks a continuous symmetry. The case of S = 1/2 anisotropic Heisenberg antiferromagnets is complicated [2]. Experiments on low dimensional magnets with negligible interactions between the magnetic chains or planes are rare. The magnetic-field-induced change in the excitation spectrum of 1D Heisenberg chains [3,4] agrees with theory [5,6]. Field-induced magnetism has also been studied in a quasi 2D S = 1 dimer system [7]. The present experiments are on a quasi 2D, S = 1/2 magnet where the continuous symmetry is broken by a very small anisotropy and the applied magnetic field, H.is a layered spin 1/2 Heisenberg antiferromagnet with a magnetic ordering transition [8] at T N = 23 K measured [9] in H = 0. The ET molecules are arranged in a 2D lattice of singly charged dimers. The electronic band is effectively half filled and the system is on the insulating side of a nearby metal-insulator Mott transition. The two chemically equivalent organic ET layers [10, 11], A and B (Fig. 1) are separated by Cu[N(CN) 2 ]Cl polymer sheets.The ordered state is well described by two-sublattice antiferromagnetic layers weakly coupled through the polymeric sheets [12]. The measured macroscopic parameter of the in-plane isotropic exchange, (J/2) i,j S i · S j is λM 0 = 2J/(gµ B ) = 450 T [8,13]. The magnitude of the antisymmetric Dzyaloshinskii-Moriya (DM) ex- Kagawa et al. [9] pointed out that in κ-ET 2 -Cl the DM interaction plays an important role above T N . In magnetic fields (unless parallel to the DM vector) the phase transition is replaced by a crossover. In this case the AF magnetization remains finite above T N and there is a weak ferromagnetic moment along H at all temperatures. They measured µ s , the field-induced staggered static magne...