We analyze platform competition where user data is collected to improve ad-targeting. Considering that users incur privacy costs, we show that the equilibrium level of data provision is distorted and can be inefficiently high or low: if overall competition is weak or if targeting benefits are low, too much private data is collected, and vice-versa. Further, we find that softer competition on either market side leads to more data collection, which implies substitutability between competition policy measures on both market sides. Moreover, if platforms engage in two-sided pricing, data provision is efficient.