The Slug Nebula is one of the largest and most luminous Lyman-alpha (LyA) nebulae discovered to date, extending over 450 kiloparsecs (kpc) around the bright quasar UM287 at z=2.283. Characterized by high surface brightnesses over intergalactic scales, its LyA emission may either trace high-density ionized gas ("clumps") or large column densities of neutral material. To distinguish between these two possibilities, information from a non-resonant line such as Halpha is crucial. Therefore, we analyzed a deep MOSFIRE observation of one of the brightest LyA emitting regions in the Slug Nebula with the goal of detecting associated Halpha emission. We also obtained a deep, moderate resolution LyA spectrum of the nearby brightest region of the Slug. We detected an Halpha flux of F_(Halpha)= 2.62 +/- 0.47 x 10^-17 erg/cm^2/s (SB_(Halpha)=2.70 +/- 0.48 x 10^-18 erg/cm^2/s/sq") at the expected spatial and spectral location. Combining the Halpha detection with its corresponding LyA flux (determined from the narrow-band imaging) we calculate a flux ratio of F_(LyA_/F_(Halpha)= 5.5 +/- 1.1. The presence of a skyline at the location of the Halpha emission decreases the signal to noise ratio of the detection and our ability to put stringent constraints on the Halpha kinematics. Our measurements argue for the origin of the LyA emission being recombination radiation, suggesting the presence of high-density ionized gas. Finally, our high-resolution spectroscopic study of the LyA emission does not show evidence of a rotating disk pattern and suggest a more complex origin for at least some parts of the Slug Nebula.