The motion of a single hole in a two-dimensional triangular antiferromagnet is investigated using the (Formula presented) model. The one-hole states are described by strings of spin deviations around the hole. Using projection technique the one-hole spectral function is calculated. For large (Formula presented) we find low-lying quasiparticlelike bands which are well separated from an incoherent background by a gap of order J. However, for small (Formula presented) this gap vanishes and the spectrum becomes broad over an energy range of several t. The results are compared with self-consistent Born approximation calculations and numerical data.