  This is a series of two papers in which we solve the Clemens conjecture:
there are only finitely many smooth rational curves of each degree in a generic
quintic threefold. In this first paper, we deal with a family of smooth
Calabi-Yau threefolds f_\epsilon for a small complex number \epsilon. We give
an geometric obstruction, deviated quasi-regular deformations B_b of
c_\epsilon, to a deformation of the rational curve c_\epsilon in a Calabi-Yau
threefold f_\epsilon.
