Like Samuel, I know this is a bit old, but the documentation for the function Grad gives an even simpler solution, by simple repeated application (and which allows use of curvilinear coordinates etc etc): Grad[Grad[f[x,y,z],{x,y,z}],{x,y,z}]

Like Samuel, I know this is a bit old, but the documentation for the function Grad gives an even simpler solution, by simple repeated application (and which allows use of curvilinear coordinates etc.):

Grad[Grad[f[x,y,z],{x,y,z}],{x,y,z}]