  We present a new finite-temperature quantum Monte Carlo algorithm to compute
imaginary-time Green functions for a single hole in the t-J model on
non-frustrated lattices. Spectral functions are then obtained with the Maximum
Entropy method. Simulations of the one-dimensional case show that a simple
charge-spin separation Ansatz is able to describe the overall features of the
spectral function over the whole energy range for values of J/t from 1/3 to 4.
This includes the bandwidth W \sim 4t + J and the compact support of the
spectral function. The quasiparticle weight Z_k is computed on lattices up to
L=96 sites, and scales as Z_k\propto L^{-1/2}.
