This paper concerns an efficient algorithm for learning in the limit of a special type of regular languages called locally testable languages from positive data, and its application to identifying the protein α-chain region in amino acid sequences. First, we present a linear time algorithm that, given a locally testable language, learns (identifies) its deterministic finite state automaton in the limit from only positive data. This provides us with a practical and efficient learning method for a specific domain of symbolic analysis. We then describe several experimental results using the learning algorithm developed above. Following a theoretical observation which strongly suggests that a certain type of amino acid sequences can be expressed by a locally testable language, we apply the learning algorithm to identifying the protein α-chain region in amino acid sequences for hemoglobin. Experimental scores show an overall success rate of 95% correct identification for positive data, and 96% for negative data.