Reconfigurable intelligent surface (RIS) is a newly-emerged technology that, with its unique features, is considered to be a game changer for future wireless networks. Channel estimation is one of the most critical challenges for the realization of RIS-assisted communications. Non-parametric channel estimation techniques are inefficient due to the huge pilot dimensionality that stems from the large number of RIS elements. The challenge becomes more serious if we consider the mobility of the users where the channel needs to be re-estimated whenever the user moves to a new location. This paper develops a novel maximum likelihood estimator (MLE) for jointly estimating the line-of-sight (LOS) channel from the user to the RIS and the direct channel between the user and the base station. By smartly refining the RIS configuration during the channel estimation procedure, we show that the channels can be accurately estimated with only a few pilot transmissions-much fewer than the number of RIS elements. The proposed scheme is also shown to be capable of effectively tracking the channel when the user moves around in a continuous but non-stationary manner with varying LOS angles,