Nanophotonic chip coupling using an optical thin-film stack forming a micro graded-refractive-index (GRIN) lens with a super-high numerical aperture (NA) that is highly compact (tens of micron long) and can be directly integrated is presented. We explore the lens' integration on the surface of Silicon-On-Insulator (SOI) platform with an asymmetric GRIN profile. We show that to achieve high efficiency for optical coupling between an optical fiber and a nanophotonic waveguide with a sub-wavelength (lambda/n) beam size, conventional asymmetric parabolic GRIN profile is no longer adequate due to the super-high NA needed (>3.1), which results in severe spatial beam aberration at the focal plane. We present an efficient algorithm to computationally generate the ideal GRIN profile that is completely aberration free even at super-high NA, which improves the coupling efficiency from ~66% (parabolic case) to ~95%. A design example involving an optical thin-film stack using an improved dual-material approach is given. The performance of the thin-film stack is analyzed. This thin-film stack based GRIN lens is shown to be high in coupling efficiency, wavelength insensitive and compatible with standard thin-film process.