  We give a new construction of higher arithmetic Chow groups for
quasi-projective arithmetic varieties over a field. Our definition agrees with
the higher arithmetic Chow groups defined by Goncharov for projective
arithmetic varieties over a field. These groups are the analogue, in the
Arakelov context, of the higher algebraic Chow groups defined by Bloch. The
degree zero group agrees with the arithmetic Chow groups of Burgos. Our new
construction is shown to be a contravariant functor and is endowed with a
product structure, which is commutative and associative.
