We present a novel physical-layer secure communications scheme based on a chirp-permuted variant of the affine frequency division multiplexing (AFDM) waveform recently proposed for sixth-generation (6G) systems, which ensures that eavesdroppers unaware of the correct chirp-permutation face significant challenges in signal detection, even with perfect channel state information (CSI) and co-location with the legitimate user. The security of the proposed scheme is studied in terms of the complexity required to find the correct permutation via classical and quantum search algorithms, analytically shown to be infeasible in both cases due to the factorially-scaling search space, and the probability of breach under the random-guess approach, also shown to be negligible.