The quaternion number system extends the complex numbers. The set of all quaternions  forms a four-dimensional associative normed division algebra over the real numbers. Quaternion valued stochastic processes received attention in the literature over the last few years. Researchers focused on generalizing the classical notions of stochastic processes in the framework of quaternion analysis. In this context, random variables are defined in the setting of quaternion analysis in many surveys. On the other hand, one of the most important and applicable stochastic process is the fractional Brownian motion. It is a Gaussian extension of the classical Brownian motion which is non-Markovian nor a semimartingale. In this paper we investigate a quaternion version of the fractional Brownian motion.