We propose a model to analyze competition between an on-line course and a traditional brick-and-mortar supply for higher education. The brick and mortar supplier is physically located and students pay a transportation cost to attend the traditional course. On the contrary, the on-line course is free, without transportation cost but students incurred a fixed homogeneous disutility when choosing this type of course. We derive the optimal fee policy of a single university as a function of its location and the fixed cost associated with the on-line course. We also study the impact of distant learning on the competition between two brick and mortar universities. One university is assumed to enjoy a central position, whereas the other one is located at the extreme left of the town. We discuss equilibria and market sharing in non-regulated (i.e pure fee competition) and regulated (i.e. quantity competition) settings. Finally, public issues are addressed. In particular, the socially optimal provision of MOOC and the supply of MOOC by universities are carefully discussed.