Enhanced aacPlus is an audio codec which is composed of advanced audio coding (AAC), spectral band replication (SBR), and parametric stereo (PS) for efficient audio coding at low bit rates. We propose a new coding scheme for lossless bit rate reduction of PS in enhanced aacPlus. We first determine the optimal contexts for context-based coding of quantized stereo parameter indexes in PS. Then we propose a coding scheme which is based on context-based coding using the determined optimal contexts in conjunction with arithmetic coding. The proposed scheme has normal and memory-reduced versions, both of which are shown to guarantee significant and consistent lossless bit rate reduction of PS. The saved bits by the proposed scheme can be used for the other modules of enhanced aacPlus, AAC and SBR.