Recent wide-field integral-field spectroscopy has revealed the detailed properties of high-redshift Ly alpha nebulae, most often targeted due to the presence of an active galactic nucleus (AGN). Here, we use VLT/MUSE to resolve the morphology and kinematics of a nebula initially identified due to strong Ly alpha emission at z similar to 3.2 (LABn06). Our observations reveal a two-lobed Ly alpha nebula, at least similar to 173 pkpc in diameter, with a light-weighted centroid near a mid-infrared source (within approximate to 17.2 pkpc) that appears to host an obscured AGN. The Ly alpha emission near the AGN is also coincident in velocity with the kinematic center of the nebula, suggesting that the nebula is both morphologically and kinematically centered on the AGN. Compared to AGN-selected Ly alpha nebulae, the surface-brightness profile of this nebula follows a typical exponential profile at large radii (>25 pkpc), although at small radii, the profile shows an unusual dip at the location of the AGN. The kinematics and asymmetry are similar to, and the C iv and He ii upper limits are consistent with, other AGN-powered Ly alpha nebulae. Double-peaked and asymmetric line profiles suggest that Ly alpha resonant scattering may be important in this nebula. These results support the picture of the AGN being responsible for powering a Ly alpha nebula that is oriented roughly in the plane of the sky. Further observations will explore whether the central surface-brightness depression is indicative of either an unusual gas or dust distribution or variation in the ionizing output of the AGN over time.