A Markov chain is a discrete-valued Markov process; discrete-valued means that the state space of possible values of the Markov chain is finite or countable. This paper seeks to forecast stock market prices using Markov Chain Model (MCM). A discrete state space is defined for an MCM which is used to calculate fitting probability matrices. Time series data of day closing prices of KenGen Company as listed in the Nairobi Stock Exchange for the period 4th January, 2016 to 31st August 2018, will be used. One of the advantages of this forecasting technique is its flexibility whereby it just requires the ability to calculate the probability at any given point. Numerical analysis is done using R. This forecasting technique is useful, not only to KenGen Company, but also to other companies listed in the NSE, the share brokers as well as the shareholders, and any other individual or company interested in trading in the share market.