  We construct the component action and supersymmetry transformations of the
$\mathcal{N} = 3$ Chern-Simons-Yang-Mills theory that flows in the infra red to
the $\mathcal{N} = 3$ super conformal quiver Chern-Simons gauge theory obtained
by Jafferis and Tomasiello in \cite{Jafferis:2008qz}. We then obtain classical
$\frac{1}{3}$-BPS (and anti-BPS) solutions all along the RG flow. The solutions
display a rich structure, for example, there is a non-trivial moduli space.
Various properties of supersymmetric monopole operators in the infra red super
conformal field theory, such as global charges and scaling dimensions can be
derived from the monopole solutions we obtain in this paper; along the lines of
the work of Benna, Klebanov and Klose in \cite{Benna:2009xd}.
