  This is the first part of the article we promised at the end of [FOOO13,
Section 1]. We discuss the foundation of the virtual fundamental chain and
cycle technique, especially its version appeared in [FOn] and also in [FOOO4,
Section A1, Section 7.5], [FOOO7, Section 12], [Fu2]. In Part 1, we focus on
the construction of the virtual fundamental chain on a single space with
Kuranishi structure. We mainly discuss the de Rham version and so work over
$\mathbb R$-coefficients, but we also include a self-contained account of the
way how to work over $\mathbb Q$-coefficients in case the dimension of the
space with Kuranishi structure is $\le 1$.
  Part 1 of this document is independent of our earlier writing [FOOO13]. We
also do not assume the reader have any knowledge on the pseudo-holomorphic
curve, in Part 1.
  Part 2 (resp. Part 3), which will appear in the near future, discusses the
case of a system of Kuranishi structures and its simultaneous perturbations
(resp. the way to implement the abstract story in the study of moduli spaces of
pseudo-holomorphic curves).
