  We implement the conformal bootstrap program for three-dimensional CFTs with
$\mathcal{N}=2$ supersymmetry and find universal constraints on the spectrum of
operator dimensions in these theories. By studying the bounds on the dimension
of the first scalar appearing in the OPE of a chiral and an anti-chiral
primary, we find a kink at the expected location of the critical
three-dimensional $\mathcal{N}=2$ Wess-Zumino model, which can be thought of as
a supersymmetric analog of the critical Ising model. Focusing on this kink, we
determine, to high accuracy, the low-lying spectrum of operator dimensions of
the theory.
