We consider a viscous drop, loaded with an insoluble surfactant,spreading over a flat plane that is covered initially with a thin liquid film. An interesting phenomenon during this spreading process is the occurrence of a dendritic fingering instability at the edge of the drop. Understanding the physical mechanisms driving this instability, using high-resolution numerical simulations along with large time asymptotics, will be the main goal of this talk. This work was done in collaboration with Oliver Jensen at Nottingham University.