  We construct the first nontrivial examples of Calabi-Yau monopoles. Our main
interest on these, comes from Donaldson and Segal's suggestion
\cite{Donaldson2009} that it may be possible to define an invariant of certain
noncompact Calabi-Yau manifolds from these gauge theoretical equations. We
focus on the Stenzel metric on the cotangent bundle of the $3$-sphere $T^*
\mathbb{S}^3$ and study monopoles under a symmetry assumption. Our main result
constructs the moduli of these symmetric monopoles and shows that these are
parametrized by a positive real number known as the mass of the monopole. In
other words, for each fixed mass we show that there is a unique monopole which
is invariant in a precise sense. Moreover, we also study the large mass limit
under which we give precise results on the bubbling behavior of our monopoles.
Towards the end an irreducible $SU(2)$ Hermitian-Yang-Mills connection on the
Stenzel metric is constructed explicitly.
