At the nanoscale, charges present at the surfaces of liquid solid interfaces greatly influence the properties of ions and molecules present in the solution, and can lead to nanoscale effects such as ion selectivity, ion current rectification, and modulation of local ionic concentrations. Concentration polarization is another nanoscale phenomenon whereby ion concentrations are enriched at one opening of an ion-selective nanopore and depleted at the other. We show that when a nanopore is in contact with a weakly soluble salt present at a concentration below its solubility product, concentration polarization can lead to locally enhanced ionic concentrations and precipitation of the salt. Formed precipitates partially or fully occlude the nanopore's opening as indicated by a measured transient decrease of the nanopore's conductance. We have identified experimental conditions at which the locally created precipitate is either pushed through or dissolved, clearing the pore entrance and allowing the precipitation reaction to occur again. The dynamic process of precipitate formation and dissolution is observed as ion current fluctuations and oscillations with frequencies reaching 200 Hz. The frequency of the system operation exceeds other nanopore-based oscillators by 2 orders of magnitude, which we believe stems from the 30 nm length of the pores examined here, versus 10 m long pores reported before.