In this thesis, we investigate lattice chiral algebras as defined by Beilinson and Drinfeld. Given a factorisation monoid satisfying specific conditions and a super extension of this, Beilinson and Drinfeld show that one can push forward this line bundle (super extension) to give a factorisation algebra. Specifically, they describe this in the case of the factorisation monoid formed by taking Г-valued divisors set-theoretically supported over each divisor, for Г a lattice, as a method of constructing these lattice chiral algebras. In this work, we show that their definitions of such divisors, and of line bundles with factorisation on these, generalise to a wider class of objects given by taking coefficients in any cone, C, in a lattice. We show that, in this more general case, the functors of C-valued divisors with settheoretic pullback contained in S are ind-schemes, and, from this, that they form a factorisation monoid. Further, we show that super line bundles with factorisation exist on this factorisation monoid, and that if we have a super line bundle with factorisation on the factorisation monoid of C-valued divisors, we can push forward such a line bundle to get a chiral (factorisation) algebra as for lattices. Hence, we obtain a new class of chiral algebras via this procedure, which we call toric chiral algebras.