Current searches for extrasolar planets have concentrated on observing the
reflex Doppler shift of solar-type stars. Little is known, however, about p
lanetary systems around nonsolar-type stars. We suggest a new method to ext
end planetary searches to hot white dwarfs. Near a hot white dwarf, the atm
osphere of a Jovian planet will be photoionized and will emit hydrogen reco
mbination lines, which may be detected by high-dispersion spectroscopic obs
ervations. Multiepoch monitoring can be used to distinguish between non-LTE
stellar emission and planetary emission and to establish the orbital param
eters of the detected planets. In the future, high-precision astrometric me
asurements of the hot white dwarf will allow the masses of the detected pla
nets to be determined. Searches for Jovian planets around hot white dwarfs
will provide invaluable new insight on the development of planetary systems
around stars more massive than the Sun and on how stellar evolution affect
s these systems. We present high-dispersion spectroscopic observations of t
he white dwarf Feige 34 to demonstrate the complexity and feasibility of th
e search method.