  The $s=1/2$ chain-boundary excitations occurring in the Haldane phaseof $s=1$
antiferromagnetic spin chains are investigated. The bilinear-biquadratic
hamiltonian is used to study these excitations as a function of the strength of
the biquadratic term, $\beta$, between $-1\le\beta\le1$. At the AKLT point,
$\beta=-1/3$, we show explicitly that these excitations are localized at the
boundaries of the chain on a length scale equal to the correlation length
$\xi=1/\ln 3$, and that the on-site magnetization for the first site is
$<S^z_1>=2/3$. Applying the density matrixrenormalization group we show that
the chain-boundaryexcitations remain localized at the boundaries for
$-1\le\beta\le1$. As the two critical points $\beta=\pm1$ are approached the
size of the $s=1/2$ objects diverges and their amplitude vanishes.
