  Soliton molecules, bound states of two solitons, can be important for the
informatics using solitons and the quest for exotic particles in a wide range
of physical systems from unconventional superconductors to nuclear matter and
Higgs field, but have been observed only in temporal dimension for classical
wave optical systems. Here, we identify a topological soliton molecule formed
spatially in an electronic system, a quasi 1D charge density wave of indium
atomic wires. This system is composed of two coupled Peierls chains, which are
endowed with a Z$_4$ topology and three distinct, right-chiral, left-chiral,
and non-chiral, solitons. Our scanning tunneling microscopy measurements
identify a bound state of right- and left-chiral solitons with distinct in-gap
states and net zero phase shift. Our density functional theory calculations
reveal the attractive interaction of these solitons and the hybridization of
their electronic states. This result initiates the study of the interaction
between solitons in electronic systems, which can provide novel manybody
electronic states and extra data-handling capacity beyond the given soliton
topology.
