  We initiate a systematic analysis of moduli spaces of vacua of four
dimensional $\mathcal{N}=3$ SCFTs. Our analysis is based on the one hand on the
properties of $\mathcal{N}=3$ chiral rings --- which we review in detail and
contrast with chiral rings of theories with less supersymmetry --- and on the
other hand on constraints coming from low-energy supersymmetry. This leads us
to introduce a new type of geometric structure, which characterizes
$\mathcal{N}=3$ SCFT moduli spaces, and that we call $triple\ special\
K\"ahler$ (TSK). A rank-$n$ TSK moduli space has complex dimension $3n$, and is
singular at complex co-dimension 3 subspaces where charged states become
massless. The structure of singularities defines a stratification of the TSK
space in terms of lower-dimensional TSK manifolds.
