Abstract: Quantum systems with gain or loss can be described by an effective non-Hermitian Hamiltonian, which results in complex energies and special degeneracies known as exceptional points. We experimentally realize such an effective non-Hermitian Hamiltonian in a single dissipative qubit comprised of a superconducting circuit and an engineered electromagnetic environment. By tuning the Hamiltonian parameters near the exceptional point degeneracy, novel forms of control and enhanced sensitivity can be obtained.