We present here a very fast, responsive fiber optic relative humidity (RH) sensor. The sensor was obtained by coating a thin PVA/CoCl2 film on the core of a plastic cladding fiber; the film was deposited after removing the cladding of the fiber. The sensor response is very fast even to a slight change in relative humidity and has a good dynamical range. The sensor is quite repeatable and fully reversible. The performance of the sensor was compared against a commercially available relative humidity sensor and was found to be sensitive to RH ranging from 3 to 90%. The sensor developed was found to be faster than the commercially available sensor in the higher humidity range. The time stability of the sensor has also been checked and was found suitable for a long term monitoring application. The sensor should be quite useful for monitoring RH in harsh industrial environments.