  CHL compactifications are supersymmetry preserving orbifolds of any
perturbatively renormalizable and ultraviolet finite ground state of the
perturbative string theories: heterotic, type I, or type II, preserving 32, 16,
12, 8, 4, (or zero) supersymmetries, and retaining the perturbative
renormalizability and finiteness of the parent string vacuum. In this paper, we
review the genesis of the CHL (Chaudhuri-Hockney-Lykken) project within the
broader context of the full String/M Duality web, establishing the existence of
moduli spaces with a small number of massless scalar fields, the
decompactification of such moduli spaces to one of the five ten-dimensional
superstring theories, and the appearance of electric-magnetic duality in only
the four-dimensional moduli spaces, a 1995 observation due to Chaudhuri &
Polchinski. We present two mathematical curiosities easily deduced from the
fermionic current algebra representation but whose physical significance is a
puzzle: a 4D N=4 heterotic string vacuum with no massless scalar fields other
than the dilaton, and a 2D N=8 heterotic string vacuum with no abelian gauge
fields, reiterating once more the necessity for a systematic classification of
the CHL orbifolds.
