We design CIS-BWE, a novel adversarial Bandwidth Extension (BWE) framework that introduces two chaos-informed discriminators -Multi-Resolution Lyapunov Discriminator (MRLD) and Multi-Scale Detrended Fractal Analysis Discriminator (MSDFA) -for capturing the deterministic chaos from speech.MRLD exploits Lyapunov exponents to capture nonlinear chaotic fluctuations.MSDFA exploits detrended fluctuation analysis to quantify fractal-like, long-range temporal chaotic correlations.To the best of our knowledge, MRLD and MSDFA are included here for the first time with a complex-valued adversarial network to explore the chaotic study of speech reconstruction.We also introduce a novel complex-valued and dual-stream generator, which uses our newly proposed Con-formerNeXt as a core block with Lattice interactions, acting as a gating mechanism by enabling controlled mixing of information across streams.We extensively optimize our design across five resolutions and use depth-wise separable convolutions to make our model lightweight yet powerful.Our CIS-BWE is tested with a de facto English and French dataset for clean and noisy speech for generalization.It achieves better performance across a total of nine subjective and objective evaluation metrics with a 40x reduction in discriminator size and overall 0.5x fewer parameters, establishing a new baseline in the BWE task.