A high pressure discharge lamp can be used in a vehicle lighting device as a light source in place of a halogen lamp, and can be driven with a reduced starting voltage while being miniaturized. A gas is filled in a space between an arc tube and an outer tube of the high pressure discharge lamp, the gas being capable of dielectric barrier discharge, to reduce the starting voltage. A metal conductor is arranged in the space between the arc tube and the outer tube to stabilize the starting voltage and perform other functions. The metal conductor can also serve as a lead line. Accordingly, high voltage portions of the lamp are not exposed outside of the outer tube. This can reduce the entire size of the high pressure discharge lamp such that a housing for a headlight using a halogen lamp can be used for this type of high pressure discharge lamp.