  We present near infra-red (NIR) adaptive optics assisted spectroscopic
observations of the CO ($\Delta\mu=2$) absorption bands towards the centre of
the giant elliptical galaxy NGC 1399. The observations were made with
NAOS-CONICA (ESO VLT) and have a FWHM resolution of 0\farcs15 (14pc). Kinematic
analysis of the observations reveals a decoupled core and strongly non-Gaussian
line-of-sight velocity profiles (VPs) in the central 0.2 arcsec (19pc). NIR
imaging also indicates an asymmetric elongation of the central isophotes in the
same region.
  We use spherical orbit-superposition models to interpret the kinematics,
using a set of orthogonal ``eigenVPs'' that allow us to fit models directly to
spectra. The models require a central black hole of mass
$1.2^{+0.5}_{-0.6}\times10^9M_\odot$, with a strongly tangentially biased orbit
distribution in the inner 40pc.
