Three-pion interferometry is investigated for new information on the space-
time structure of the pion source created in ultrarelativistic heavy-ion co
llisions. The two- and three-pion correlations are numerically computed for
incoherent source functions based on the Bjorken hydrodynamical model, ove
r a wide range of the kinematic variables. New information provided by thre
e-pion interferometry, different from that provided by two-pion interferome
try, should appear in the phases of the Fourier transform of the source fun
ction. Variables are identified that would be sensitive to the phases and s
uitable for observation. For a positive, chaotic source function, however,
a variation of the three-pion phase is found to be difficult to extract fro
m experiments. Effects of asymmetry of the source function are also examine
d. [S0556-2813(99)00112-0].