There are only two quantum group structures on the space of two by two unimodular matrices, these are the SL
q
(2) and the SL
h
(2) quantum groups. The differential geometry of SL
q
(2) is well known. In this Letter, we develop the differential geometry of SL
h
(2), and show that the space of left invariant vector fields is three-dimensional.
Mathematics Subject Classifications (1991) 81R50 - 16W30 - 58B30