  We report on the discovery of a new Milky Way (MW) satellite in Bo\"otes
based on data from the on-going Hyper Suprime-Cam (HSC) Subaru Strategic
Program (SSP). This satellite, named Bo\"otes IV, is the third ultra-faint
dwarf that we have discovered in the HSC-SSP. We have identified a
statistically significant (32.3$\sigma$) overdensity of stars having
characteristics of a metal-poor, old stellar population. The distance to this
stellar system is $D_{\odot}=209^{+20}_{-18}$ kpc with a $V$-band absolute
magnitude of $M_V=-4.53^{+0.23}_{-0.21}$ mag. Bo\"otes IV has a half-light
radius of $r_h=462^{+98}_{-84}$ pc and an ellipticity of
$0.64^{+0.05}_{-0.05}$, which clearly suggests that this is a dwarf satellite
galaxy. We also found another overdensity that appears to be a faint globular
cluster with $M_V=-0.20^{+0.59}_{-0.83}$ mag and $r_h=5.9^{+1.5}_{-1.3}$ pc
located at $D_{\odot}=46^{+4}_{-4}$ kpc. Adopting the recent prediction for the
total population of satellites in a MW-sized halo by Newton et al. (2018),
which combined the characteristics of the observed satellites by SDSS and DES
with the subhalos obtained in $\Lambda$CDM models, we estimate that there
should be about two MW satellites at $M_V\le0$ in the $\sim676$ deg$^2$ covered
by HSC-SSP, whereas that area includes six satellites. Thus, the observed
number of satellites is larger than the theoretical prediction. On the face of
it, we have a problem of too many satellites, instead of the well-known missing
satellites problem whereby the $\Lambda$CDM theory overpredicts the number of
satellites in a MW-sized halo. This may imply that the models need more
refinements for the assignment of subhalos to satellites such as considering
those found by the current deeper survey. [abridged]
