In steganography, secret data are invisible in cover media, such as text, audio, video and image. Hence, attackers have no knowledge of the original message contained in the media or which algorithm is used to embed or extract such message. Image steganography is a branch of steganography in which secret data are hidden in host images. In this study, image steganography using least significant bit and secret map techniques is performed by applying 3D chaotic maps, namely, 3D Chebyshev and 3D logistic maps, to obtain high security. This technique is based on the concept of performing random insertion and selecting a pixel from a host image. The proposed algorithm is comprehensively evaluated on the basis of different criteria, such as correlation coefficient, information entropy, homogeneity, contrast, image, histogram, key sensitivity, hiding capacity, quality index, mean square error (MSE), peak signal-to-noise ratio (PSNR) and image fidelity. Results show that the proposed algorithm satisfies all the aforementioned criteria and is superior to other previous methods. Hence, it is efficient in hiding secret data and preserving the good visual quality of stego images. The proposed algorithm is resistant to different attacks, such as differential and statistical attacks, and yields good results in terms of key sensitivity, hiding capacity, quality index, MSE, PSNR and image fidelity.