  This is the first of a series of two papers devoted to the partition function
realization of Wilson surfaces in strict higher gauge theory. A higher version
of the Kirillov-Kostant-Souriau theory of coadjoint orbits is presented based
on the derived geometric framework, which has shown its usefulness in
4--dimensional higher Chern--Simons theory. An original notion of derived
coadjoint orbit is put forward. A theory of derived unitary line bundles and
Poisson structures on regular derived orbits is constructed. The proper derived
counterpart of the Bohr--Sommerfeld quantization condition is then identified.
A version of derived prequantization is proposed. The difficulties hindering a
full quantization, shared with other approaches to higher quantization, are
pinpointed and a possible way--out is suggested. The theory we elaborate
provide the geometric underpinning for the field theoretic constructions of the
companion paper.
