Speech signals can be considered as being generated by a mechanical system with inherently nonlinear dynamics. The justification for this comment is apparent when one considers the production of speech. We make use of the largest Lyapunov exponent which estimates the amount of chaos in a system. The largest Lyapunov exponent was calculated for a variety of Spanish voiced sounds (nasals and vowels) using the method suggested by M.T. Rosenstein et al. (see Physica D, vol.65, p.117-34, 1993). The presence of the positive largest Lyapunov exponent proves the chaotic nature of these speech signals and places limits on their predictability.