  This paper is for the proceedings of the Chen-Chow Conference held in
Tianjin, China in October 2000. The goal of the paper is to produce and survey
evidence for a connection between Chen's work on iterated integrals on the one
hand, and algebraic cycles and motives on the other. The paper is expository,
and begins with an introduction to Chen's work. Topics covered include loop
space de Rham theorems; iterated integrals of currents; the works of
Carlson-Clemmens-Morgan and Bruno Harris on periods of mixed Hodge structures
on homotopy groups and algebraic cycles; the cobar construction, algebraic
loopspace de Rham Theorems; and generalized iterated integrals.
