  We promote geometric prequantization to higher geometry (higher stacks),
where a prequantization is given by a higher principal connection (a higher
gerbe with connection). We show fairly generally how there is canonically a
tower of higher gauge groupoids and Courant groupoids assigned to a higher
prequantization, and establish the corresponding Atiyah sequence as an
integrated Kostant-Souriau infinity-group extension of higher Hamiltonian
symplectomorphisms by higher quantomorphisms. We also exhibit the
infinity-group cocycle which classifies this extension and discuss how its
restrictions along Hamiltonian infinity-actions yield higher Heisenberg
cocycles. In the special case of higher differential geometry over smooth
manifolds we find the L-infinity-algebra extension of Hamiltonian vector fields
-- which is the higher Poisson bracket of local observables -- and show that it
is equivalent to the construction proposed by the second author in n-plectic
geometry. Finally we indicate a list of examples of applications of higher
prequantization in the extended geometric quantization of local quantum field
theories and specifically in string geometry.
