We develop a model to study the observability of investors' information acquisition in financial markets. Relative to observable information acquisition, unobservable information acquisition leads to more information production if and only if the ratio of the information-acquisition cost to noise trading is relatively high. This information-production result has further consequences for market quality. When we allow investors to endogenously choose the observability of their information acquisition behavior, their equilibrium choices are always characterized by a prisoner's dilemma. Our analysis has implications for financial regulations on investors' private meetings with company management and the practice of tracing the digital footprints of investors.