  We present a detailed analysis of new ALMA observations of the disk around
the T-Tauri star HD 143006, which at 46 mas (7.6 au) resolution reveal new
substructures in the 1.25 mm continuum emission. The disk resolves into a
series of concentric rings and gaps together with a bright arc exterior to the
rings that resembles hydrodynamics simulations of a vortex, and a bridge-like
feature connecting the two innermost rings. Although our $^{12}$CO observations
at similar spatial resolution do not show obvious substructure, they reveal an
inner disk depleted of CO emission. From the continuum emission and the CO
velocity field we find that the innermost ring has a higher inclination than
the outermost rings and the arc. This is evidence for either a small
($\sim8^{\circ}$) or moderate ($\sim41^{\circ}$) misalignment between the inner
and outer disk, depending on the specific orientation of the near/far sides of
the inner/outer disk. We compare the observed substructures in the ALMA
observations with recent scattered light data from VLT/SPHERE of this object.
In particular, the location of narrow shadow lanes in the SPHERE image combined
with pressure scale height estimates, favor a large misalignment of about
$41^{\circ}$. We discuss our findings in the context of a dust-trapping vortex,
planet-carved gaps, and a misaligned inner disk due to the presence of an
inclined companion to HD 143006.
