  We present an observation of $B\to\eta^\prime K^*$. The data sample
corresponds to 232 million $B\bar{B}$ pairs collected with the BABAR detector
at the PEP-II asymmetric-energy $B$ Factory at SLAC. We measure the branching
fractions (in units of $10^{-6}$) $\mathcal{B}(B^0\to\eta^\prime K^{*0}) =
3.8\pm1.1\pm0.5$ and $\mathcal{B}(B^+\to\eta^\prime K^{*+}) =
4.9^{+1.9}_{-1.7}\pm0.8$, where the first error is statistical and the second
systematic. A simultaneous fit results in the observation of $B\to\eta^\prime
K^*$ with $\mathcal{B}(B\to\eta^\prime K^*) = 4.1_{-0.9}^{+1.0} \pm 0.5$. We
also search for $B\to\eta^\prime \rho$ and $B\to\eta^\prime f_0(980)(f_0 \to
\pi^+\pi^-)$ with results and 90% confidence level upper limits
$\mathcal{B}(B^+\to\eta^\prime \rho^+) = 8.7^{+3.1}_{-2.8}{} ^{+2.3}_{-1.3}$
($<14$), $\mathcal{B}(B^0\to\eta^\prime \rho^0) < 3.7$ and
$\mathcal{B}(B^0\to\eta^\prime f_0(980)(f_0\to\pi^+\pi^-)) < 1.5$. Charge
asymmetries in the channels with significant yields are consistent with zero.
