We present integral field spectrograph (IFS) with laser guide star adaptive optics (LGS-AO) observations of z∼2 quasi-stellar objects (QSOs) designed to resolve extended nebular line emission from the host galaxy. Our data was obtained with W. M. Keck and Gemini-North Observatories using OSIRIS and NIFS coupled with the LGS-AO systems, respectively. We have conducted a pilot survey of five QSOs, three observed with NIFS+AO and two observed with OSIRIS+AO at an average redshift of z=2.2. We demonstrate that the combination of AO and IFSs provides the necessary spatial and spectral resolutions required to separate QSO emission from its host. We present our technique for generating a PSF from the broad-line region of the QSO and performing PSF subtraction of the QSO emission to detect the host galaxy emission at separation of ∼0.2 ′′ (∼1.4 kpc). We detect Hα narrow-line emission for two sources, SDSSJ1029+6510 (z Hα =2.182) and SDSSJ0925+0655 (z Hα =2.197), that have evidence for both star formation and extended narrow-line emission. Assuming that the majority of narrow-line Hα emission is from star formation, we infer a star formation rate for SDSSJ1029+6510 of 78.4 M ⊙ yr −1 originating from a compact region that is kinematically offset by 290 -350 km s −1 . For SDSSJ0925+0655 we infer a star formation rate of 29 M ⊙ yr −1 distributed over three clumps that are spatially offset by ∼ 7 kpc. The null detections on three of the QSOs are used to infer surface brightness limits and we find that at 1.4 kpc from the QSO the un-reddened star formation limit is 0.3 M ⊙ yr −1 kpc −2 . If we assume typical extinction values for z=2 type-1 QSOs, the dereddened star formation rate for our null detections would be 0.6 M ⊙ yr −1 kpc −2 . These IFS observations indicate that while the central black hole is accreting mass at 10-40% of the Eddington rate, if star formation is present in the host (1.4 -20 kpc) it would have to occur diffusely with significant extinction and not in compact, clumpy regions.