  We demonstrate a continuously loaded $^{88}\mathrm{Sr}$ magneto-optical trap
(MOT) with a steady-state phase-space density of $1.3(2) \times 10^{-3}$. This
is two orders of magnitude higher than reported in previous steady-state MOTs.
Our approach is to flow atoms through a series of spatially separated laser
cooling stages before capturing them in a MOT operated on the 7.4-kHz linewidth
Sr intercombination line using a hybrid slower+MOT configuration. We also
demonstrate producing a Bose-Einstein condensate at the MOT location, despite
the presence of laser cooling light on resonance with the 30-MHz linewidth
transition used to initially slow atoms in a separate chamber. Our steady-state
high phase-space density MOT is an excellent starting point for a continuous
atom laser and dead-time free atom interferometers or clocks.
