We introduce the chemical potential in a system of two-flavored massless fe
rmions in a chiral bag, with an external Skyrmion, by imposing boundary con
ditions in the Euclidean time direction. We express the fermionic mean numb
er in terms of a functional trace involving the Green function of the bound
ary value problem, which is studied analytically. Numerical evaluations for
the fermionic number are presented. [S0556-2813(99)04310-1].