  Determinations of the primordial helium abundance are used in precision
cosmological tests. These require highly accurate He I recombination rate
coefficients. Here we reconsider the formation of He I recombination lines in
the low-density limit. This is the simplest case and it forms the basis for the
more complex situation where collisions are important. The formation of a
recombination line is a two-step process, beginning with the capture of a
continuum electron into a bound state and followed by radiative cascade to
ground. The rate coefficient for capture from the continuum is obtained from
photoionization cross sections and detailed balancing, while radiative
transition probabilities determine the cascades. We have made every effort to
use today's best atomic data. Radiative decay rates are from Drake's
variational calculations, which include QED, fine structure, and
singlet-triplet mixing. Certain high-$L$ fine-structure levels do not have a
singlet-triplet distinction and the singlets and triplets are free to mix in
dipole-allowed radiative decays. We use quantum defect or hydrogenic
approximations to include levels higher than those treated in the variational
calculations. [Abstract clipped]
