We report on the discovery of a new Milky Way (MW) satellite in Bootes based on data from the on-going Hyper Suprime-Cam (HSC) Subaru Strategic Program (SSP). This satellite, named Bootes 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. Bootes 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 $M_Vle0$ 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]
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