  The LIGO/Virgo detected a gravitational wave (GW) event, named
GW200224_222234 (a.k.a. S200224ca) and classified as a binary-black-hole
coalescence, on February 24, 2020. Given its relatively small localization
skymap (71 deg$^2$ for a 90% credible region; revised to 50 deg$^2$ in GWTC-3),
we performed target-of-opportunity observations using the Subaru/Hyper
Suprime-Cam (HSC) in the $r2$- and $z$-bands. Observations were conducted on
February 25 and 28 and March 23, 2020, with the first epoch beginning 12.3 h
after the GW detection. The survey covered the highest probability sky area of
56.6 deg$^2$, corresponding to a 91% probability. This was the first deep
follow-up ($m_{r}\gtrsim24, m_{z}\gtrsim23$) for a binary-black-hole merger
covering $>$90% of the localization. By performing image subtraction and
candidate screening including light curve fitting with transient templates and
examples, we found 22 off-nucleus transients that were not ruled out as the
counterparts of GW200224_222234 with only our Subaru/HSC data. We also
performed GTC/OSIRIS spectroscopy of the probable host galaxies for five
candidates; two are likely to be located within the 3D skymap, whereas the
others are not. In conclusion, 19 transients remain as possible optical
counterparts of GW200224_222234; however, we could not identify a unique
promising counterpart. If there are no counterparts in the remaining
candidates, the upper limits of optical luminosity are $\nu L_{\nu} <
5.2^{+2.4}_{-1.9}\times 10^{41}$ erg s$^{-1}$ and $\nu L_{\nu} <
1.8^{+0.8}_{-0.6}\times 10^{42}$ erg s$^{-1}$ in the $r2$- and $z$-bands,
respectively, at $\sim$12 h after GW detection. We also discuss improvements in
the strategies of optical follow-ups for future GW events.
