Inertial odometry (IO) relies exclusively on signals from an inertial measurement unit (IMU) for localization and offers a promising avenue for consumer grade positioning. However, accurate modeling of the nonlinear motion patterns present in IMU signals remains the principal limitation on IO accuracy. To address this challenge, we propose CKANIO, an IO framework that integrates Chebyshev based Kolmogorov-Arnold Networks (Chebyshev KAN). Specifically, we design a novel residual architecture that leverages the nonlinear approximation capabilities of Chebyshev polynomials within the KAN framework to more effectively model the complex motion characteristics inherent in IMU signals. To the best of our knowledge, this work represents the first application of an interpretable KAN model to IO. Experimental results on five publicly available datasets demonstrate the effectiveness of CKANIO.