Chimera states are spatiotemporal patterns in which phase-locked oscillators coexist with drifting ones, first discovered in arrays of coupled oscillators. These states are believed to occur only in systems with nonlocal coupling, not in locally or globally coupled systems. This paper presents an exact solution for chimera states in a ring of phase oscillators coupled by a cosine kernel. The stable chimera state bifurcates from a spatially modulated drift state and dies in a saddle-node bifurcation with an unstable chimera. Chimera states are characterized by two domains: one coherent and phase-locked, the other incoherent and desynchronized. Unlike previous states, all oscillators are identical, and the chimera state is not due to supercritical instability or partially locked/partially incoherent states in non-identical oscillators. The chimera state was first noticed in simulations of limit-cycle oscillators with nonlocal coupling. The paper explains the origin of chimera states and the conditions for their existence. It studies the simplest system that supports a chimera state: a ring of phase oscillators governed by a specific equation. The solution involves an exact analytical approach, leading to expressions for the order parameter and phase. The solution shows that the chimera state arises from a bifurcation of a spatially modulated drift state. The paper also presents a perturbative analysis of the chimera state, showing how the fraction of drifting oscillators changes with control parameters. The results indicate that the chimera state exists in a specific region of parameter space, with a boundary determined by a saddle-node bifurcation. The analysis also reveals the spatial structure of the chimera state, including the local coherence and average phase. The paper concludes that chimera states are a fascinating phenomenon that can occur in various spatially extended systems, including the complex Ginzburg-Landau equation with nonlocal coupling. The study provides insights into the mechanisms of pattern formation in such systems.Chimera states are spatiotemporal patterns in which phase-locked oscillators coexist with drifting ones, first discovered in arrays of coupled oscillators. These states are believed to occur only in systems with nonlocal coupling, not in locally or globally coupled systems. This paper presents an exact solution for chimera states in a ring of phase oscillators coupled by a cosine kernel. The stable chimera state bifurcates from a spatially modulated drift state and dies in a saddle-node bifurcation with an unstable chimera. Chimera states are characterized by two domains: one coherent and phase-locked, the other incoherent and desynchronized. Unlike previous states, all oscillators are identical, and the chimera state is not due to supercritical instability or partially locked/partially incoherent states in non-identical oscillators. The chimera state was first noticed in simulations of limit-cycle oscillators with nonlocal coupling. The paper explains the origin of chimera states and the conditions for their existence. It studies the simplest system that supports a chimera state: a ring of phase oscillators governed by a specific equation. The solution involves an exact analytical approach, leading to expressions for the order parameter and phase. The solution shows that the chimera state arises from a bifurcation of a spatially modulated drift state. The paper also presents a perturbative analysis of the chimera state, showing how the fraction of drifting oscillators changes with control parameters. The results indicate that the chimera state exists in a specific region of parameter space, with a boundary determined by a saddle-node bifurcation. The analysis also reveals the spatial structure of the chimera state, including the local coherence and average phase. The paper concludes that chimera states are a fascinating phenomenon that can occur in various spatially extended systems, including the complex Ginzburg-Landau equation with nonlocal coupling. The study provides insights into the mechanisms of pattern formation in such systems.