We experimentally show that an electric dipole moment of more than 1 Debye can be induced in the dysprosium (Dy) atom, in a long-lived state that is about 17513 cm[-1] above the ground state. This metastable state is part of a strongly coupled opposite-parity doublet. Using optically detected microwave spectroscopy in an atomic beam, we determine the approximately 1.12 cm[-1] doublet spacing for the five stable bosonic isotopes of Dy with kHz-level accuracy. From the shift of the microwave transition frequency in low electric fields (below 150 V/cm) and from optical spectra in high electric fields (up to 150 kV/cm), a reduced transition dipole moment of 7.65 ± 0.05 Debye between the doublet states is extracted. In high electric fields the doublet interacts with a third state at 17727 cm[-1], that connects to the ground state via an electric-dipole transition. The three-state Stark interaction enables preparation of Dy atoms in the metastable state via single-photon excitation from the ground state. Our work experimentally validates predicted characteristics of the opposite-parity doublet, and provides an effective route to the first doubly polar quantum gas of atoms.