  We present the HI emission project within the MIGHTEE survey, currently being
carried out with the newly commissioned MeerKAT radio telescope. This is one of
the first deep, blind, medium-wide interferometric surveys for neutral hydrogen
(HI) ever undertaken, extending our knowledge of HI emission to z=0.6. The
science goals of this medium-deep, medium-wide survey are extensive, including
the evolution of the neutral gas content of galaxies over the past 5 billion
years. Simulations predict nearly 3000 galaxies over 0<z<0.4 will be detected
directly in HI, with statistical detections extending to z=0.6. The survey
allows us to explore HI as a function of galaxy environment, with massive
groups and galaxy clusters within the survey volume. Additionally, the area is
large enough to contain as many as 50 local galaxies with HI mass $<10^8$ Msun,
which allows us to study the low-mass galaxy population. The 20 deg$^2$ main
survey area is centred on fields with exceptional multi-wavelength ancillary
data, with photometry ranging from optical through far-infrared wavelengths,
supplemented with multiple spectroscopic campaigns. We describe here the survey
design and the key science goals. We also show first results from the Early
Science observations, including kinematic modelling of individual sources,
along with the redshift, HI, and stellar mass ranges of the sample to date.
