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We consider compactifications of heterotic string theory to four dimensionson CHL orbifolds of the type T^6 /Z_N with 16 supersymmetries. The exactpartition functions of the quarter-BPS dyons in these models are given in termsof genus-two Siegel modular forms. Only the N=1,2,3 models satisfy a certainfiniteness condition, and in these cases one can identify a Borcherds-Kac-Moodysuperalgebra underlying the symmetry structure of the dyon spectrum. Weidentify the real roots, and find that the corresponding Cartan matricesexhaust a known classification. We show that the Siegel modular form satisfiesthe Weyl denominator identity of the algebra, which enables the determinationof all root multiplicities. Furthermore, the Weyl group determines thestructure of wall-crossings and the attractor flows of the theory. For N> 4, nosuch interpretation appears to be possible.

Borcherds-Kac-Moody Symmetry of N=4 Dyons