  We compute R-charges of the BPS-monopole operators in $\mathcal{N} = 3$
$\widehat{ADE}$ Chern-Simons quiver gauge theories, along the lines of the work
of Benna, Klebanov and Klose in \cite{bkk}. These theories have a weakly
coupled UV completion in terms of $\mathcal{N}=3$ supersymmetric Chern-Simons
Yang-Mills theories. In the UV limit the monopole operators are well
approximated by classical solutions. We construct classical BPS and anti-BPS
monopole solutions to these theories which preserve $\frac{1}{3}$ supersymmetry
all along the RG flow. We compute the $SU(2)_R$ charges in these backgrounds
and show that the smallest possible value of quantised $SU(2)_R$ charge is zero
in each quiver theory.
