We present the first systematic search for extended metal-line [O II] \ensuremathłambda\ensuremathłambda3726, 3729 nebulae, or [O II] blobs (O IIBs), at z = 1.2 using deep narrowband imaging with a survey volume of 1.9 × 10$^5$ Mpc$^3$ on the 0.62 deg$^2$ sky of Subaru-XMM Deep Survey (SXDS) field. We discover a giant O IIB, called ``O IIB 1,'' with a spatial extent over åisebox-0.5ex~75 kpc at a spectroscopic redshift of z = 1.18, and also identify a total of 12 O IIBs with a size of >30 kpc. Our optical spectrum of O IIB 1 presents [Ne V] \ensuremathłambda3426 line at the 6\ensuremathσ level, indicating that this object harbors an obscured type-2 active galactic nucleus (AGN). The presence of gas outflows in this object is suggested by two marginal detections of Fe II \ensuremathłambda2587 absorption and Fe II* \ensuremathłambda2613 emission lines both of which are blueshifted at as large as 500-600 km s$^-1$, indicating that the heating source of O IIB 1 is AGN or associated shock excitation rather than supernovae produced by starbursts. The number density of O IIB 1-type giant blobs is estimated to be \i̊sebox-0.5ex~5 × 10$^-6$ Mpc$^-3$ at z \rs̊ebox-0.5ex~ 1.2, which is comparable with that of AGNs driving outflow at a similar redshift, suggesting that giant O IIBs are produced only by AGN activity. On the other hand, the number density of small O IIBs, 6 × 10$^-5$ Mpc$^-3$, compared to that of z \rae̊box-0.5ex~ 1 galaxies in the blue cloud in the same M$_B$ range, may imply that 3% of star-forming galaxies at z \raib̊ox-0.5ex~ 1 are quenching star formation through outflows involving extended [O II] emission.