I consider M-theory compactifications on a certain family of G₂ cones built over complex three-dimensional spaces. Such spaces can be described as Kahler quotients of eight-dimensional hyperkahler cones or as the twistor spaces of certain singular, Einstein self-dual four-manifolds. Upon restricting to twistor spaces which result from so-called `toric hyperkahler cones', one obtains a double discrete infinity of G₂ models whose singularities can be analyzed explicitly. This gives a large generalization of the compactifications recently considered by E. Witten and B. Acharya. I explain the general methods and results of this analysis and show that the low energy description of these models leads to chiral gauge theories admitting an arbitrary number of SU(n) factors. Finally, I show that such M-theory compactifications admit T-dual type IIA and type IIB descriptions, which in the generic case involve both localized and delocalized branes.