Classification accuracy provided by a machine learning model depends a lot on the feature set used in the learning process. Feature selection (FS) is an important and challenging preprocessing technique which helps to identify only the relevant features from a dataset, thereby reducing the feature dimension as well as improving the classification accuracy at the same time. The binary version of whale optimization algorithm (WOA) is a popular FS technique which is inspired from the foraging behavior of humpback whales. In this paper, an embedded version of WOA called embedded chaotic whale survival algorithm (ECWSA) has been proposed which uses its wrapper process to achieve high classification accuracy and a filter approach to further refine the selected subset with low computation cost. Chaos has been introduced in the ECWSA to guide selection of the type of movement followed by the whales while searching for prey. A fitness-dependent death mechanism has also been introduced in the system of whales which is inspired from the real-life scenario in which whales die if they are unable to catch their prey. The proposed method has been evaluated on 18 well-known UCI datasets and compared with its predecessors as well as some other popular FS methods. The source code of ECWSA can be found in https://github.com/Ritam-Guha/ECWSA.