  We present the results of quantum calculations based on entirely ab initio
methods for a variety of molecular processes and chemical reactions involving
the LiHe$^+$ ionic polar molecule. With the aid of these calculations we derive
accurate reaction rates and fitting expressions valid over a range of gas
temperatures representative of the typical conditions of the pregalactic gas.
With the help of a full chemical network, we then compute the evolution of the
abundance of LiHe$^+$ as function of redshift in the early Universe. Finally,
we compare the relative abundance of LiHe$^+$ with that of other polar cations
formed in the same redshift interval.
