Steganography is widely recognized as an effective method for protecting information via digital media. This paper presents an innovative image steganography algorithm incorporating image compression, chaotic maps, and the least significant bit. The process begins with the compression of a confidential medical image using Huffman encoding. The compressed image then undergoes shuffling, facilitated by the chaotic logistic map. The bits from the shuffled image are discreetly embedded into randomly selected pixels of the cover image, guided by the chaotic piecewise smooth map. The resulting stego image is generated. Statistical analyses are applied to both the cover and stego images for evaluation. The proposed algorithm is compared against state-of-the-art algorithms, and the results demonstrate its superiority over existing methods.