This paper presents a design methodology for optimal transmission energy allocation at a sensor equipped with energy harvesting technology for remote state estimation of linear stochastic dynamical systems. In this framework, the sensor measurements as noisy versions of the system states are sent to the receiver over a packet dropping communication channel. The packet dropout probabilities of the channel depend on both the sensor's transmission energies and time varying wireless fading channel gains. The sensor has access to an energy harvesting source which is an everlasting but unreliable energy source compared to conventional batteries with fixed energy storages. The receiver performs optimal state estimation with random packet dropouts to minimize the estimation error covariances based on received measurements. The receiver also sends packet receipt acknowledgments to the sensor via an erroneous feedback communication channel which is itself packet dropping.