  The first observation of the decay $B^0_s\rightarrow\chi_{c1}\phi$ and a
study of $B^0\rightarrow\chi_{c1,2}K^{*0}$ decays are presented. The analysis
is performed using a dataset, corresponding to an integrated luminosity of 1.0
fb$^{-1}$, collected by the LHCb experiment in pp collisions at a
centre-of-mass energy of 7 TeV. The following ratios of branching fractions are
measured: \begin{equation*} \begin{array}{lll}
\dfrac{\cal{B}(B^0_s\rightarrow\chi_{c1}\phi)}{\cal{B}(B^0_s\rightarrow
J/\psi\phi)} &=& (18.9 \pm1.8\,(stat)\pm1.3\,(syst)\pm0.8\,(\cal{B})) \times
10^{-2}, \nonumber \\ \noalign{\vskip 3pt}
\dfrac{\cal{B}(B^0\rightarrow\chi_{c1}K^{*0})}{\cal{B}(B^0\rightarrow
J/\psiK^{*0})} &=& (19.8 \pm1.1\,(stat)\pm1.2\,(syst)\pm0.9\,(\cal{B})) \times
10^{-2}, \nonumber \\ \noalign{\vskip 3pt}
\dfrac{\cal{B}(B^0\rightarrow\chi_{c2}K^{*0})}{\cal{B}(B^0\rightarrow\chi_{c
1}K^{*0})} &=& (17.1 \pm5.0\,(stat)\pm1.7\,(syst)\pm1.1\,(\cal{B})) \times
10^{-2}, \nonumber \\ \noalign{\vskip 3pt} \end{array} \end{equation*}
\noindent where the third uncertainty is due to the limited knowledge of the
branching fractions of ${\chi_{c}\rightarrow J/\psi \gamma}$ modes.
