This paper studies fully distributed parameter estimation under sensor attacks. A group of agents make measurements of a bounded parameter and a fraction of the agents' sensor measurements falls under integrity attack. When a sensor is under attack, its measurement can take any value as determined by the attacker. The agents exchange messages over a communication network to ensure that all agents are able to correctly estimate the parameter of interest. This paper presents a consensus+innovations algorithm for attack resilient distributed parameter estimation. The algorithm achieves the same level of resilience as the most resilient centralized estimator - if less than half of the agents' sensors are under attack, then all agents correctly estimate the parameter of interest, regardless of the topology of the inter-agent communication network, as long as it is connected. This paper illustrates the performance of the algorithm under adversarial attack through numerical simulations.