Many physical phenomena can be understood by single-particle physics; that is, treating particles as non-interacting entities. When this fails, many-body interactions lead to spontaneous symmetry breaking and phenomena such as fundamental particles' mass generation, superconductivity and magnetism. Competition between single-particle and many-body physics leads to rich phase diagrams. Here we show that rhombohedral-stacked trilayer graphene offers an exciting platform for studying such interplay, in which we observe a giant intrinsic gap ~42 meV that can be partially suppressed by an interlayer potential, a parallel magnetic field or a critical temperature ~36 K. Among the proposed correlated phases with spatial uniformity, our results are most consistent with a layer antiferromagnetic state with broken time reversal symmetry. These results reflect the interplay between externally induced and spontaneous symmetry breaking whose relative strengths are tunable by external fields, and provide insight into other low-dimensional systems.