  Low-lying excited states as well as the ground state of the spin-1
antiferromagnetic Heisenberg chain with a spin-1/2 impurity are studied by
means of a method of numerical diagonalization. The isotropic nearest-neighbor
exchange coupling plus the uniaxial single-ion-type anisotropy energy is
assumed for the host-system Hamiltonian. The energy differences between the
ground state and the low-lying excited states, which appear in the Haldane gap,
are estimated in the thermodynamic limit. The results are used to analyze the
electron-spin-resonance experimental data on
Ni(C$_2$H$_8$N$_2$)$_2$NO$_2$(ClO$_4$), abbreviated NENP, containing a small
amount of spin-1/2 Cu$^{2+}$ impurities. It is found that in this system, the
impurity-host $\bigl($Cu$^{2+}$-Ni$^{2+}$$\bigr)$ coupling is ferromagnetic and
its magnitude is about 5$\,$\% of the magnitude of the host-host
$\bigl($Ni$^{2+}$-Ni$^{2+}$$\bigr)$ coupling.
