To explore the relation between properties of Loewner chains and properties of their driving functions, we study Loewner chains driven by functions U of finite total variation. Under a slow point condition, we show the existence of a simple trace γ and establish the continuity of the map from U to γ with respect to the uniform topology on γ and to the total variation topology on U . In the spirit of the work of Wong [19] and Lind-Tran [9], we also obtain conditions on the driving function that ensures the trace to be continuously differentiable.