  We report results of our new spatially-resolved, optical spectroscopy of the
giant Ly$\alpha$ nebula around a powerful radio galaxy 1243+036 (4C+03.24) at
$z=3.57$. The nebula is extended over $\sim 30$ kpc from the nucleus, and forms
a pair of cones or elongated bubbles. The high-velocity ($\sim -1000$ km
s$^{-1}$; blueshifted with respect to the systemic velocity)
Ly$\alpha$-emitting components are detected at both sides of the nucleus along
its major axis. The northwestern nebula is more spectacular in its velocity
shift (blueshifted by -1000 km s$^{-1}$ to -1400 km s$^{-1}$) and in its width
($\simeq 1900$ km s$^{-1}$ FWHM) over $\simeq 30$ kpc scale. We discuss
possible origin of the nebula; 1) the shock-heated expanding bubble or
outflowing cone associated with the superwind activity of the host galaxy, 2)
halo gas photoionized by the anisotropic radiation from the active galactic
nuclei (AGN), and 3) the jet-induced star-formation or shock. The last
possibility may not be likely because Ly$\alpha$ emission is distributed out of
the narrow channel of the radio jet. We show that the superwind model is most
plausible since it can explain both the characteristics of the morphology (size
and shape) and the kinematical structures (velocity shift and line width) of
the nebula although the photoionization by AGN may contribute to the excitation
to some extent.
