  The pair density wave (PDW) is an extraordinary superconducting state where
Cooper pairs carry nonzero momentum. It can emerge when the full condensation
of zero momentum Cooper pairs is frustrated. Evidence for the existence of
intrinsic PDW order in high-temperature (high-Tc) cuprate superconductors and
kagome superconductors has emerged recently. However, the PDW order in
iron-based high-Tc superconductors has not been observed experimentally. Here,
using scanning tunneling microscopy/spectroscopy, we report the discovery of
the PDW state in monolayer iron-based high-Tc Fe(Te,Se) films grown on
SrTiO3(001) substrates. The PDW state with a period of {\lambda}~3.6a_Fe (a_Fe
is the distance between neighboring Fe atoms) is observed at the domain walls
by the spatial electronic modulations of the local density of states,
superconducting gap, and the {\pi}-phase shift boundaries of the PDW around the
dislocations of the intertwined charge density wave order. The discovery of the
PDW state in the monolayer Fe(Te,Se) film provides a low-dimensional platform
to study the interplay between the correlated electronic states and
unconventional Cooper pairing in high-Tc superconductors.
