Modern electronic-support measures (ESM) increasingly employ deep-learning classifiers that exploit the deterministic, periodic structure of conventional low-probability-of-intercept (LPI) waveforms such as linear frequency-modulated continuous-wave (FMCW) signals. This paper investigates chaos-based frequency-modulated (CBFM) waveforms, generated from the Lorenz and Rössler attractors, as a countermeasure. Using a fully simulation-based framework (2 GHz sampling rate, 10 µs pulse, 500 MHz bandwidth, time–bandwidth product 5000), we compare CBFM against calibrated FMCW and band-limited noise-radar references on spectral flatness, autocorrelation peak-sidelobe ratio (PSR), ambiguity-function shape, and a newly defined inter-pulse correlation gain (IPCG) that quantifies an interceptor’s ability to reuse a previously captured pulse. Although FMCW attains the flattest spectrum (spectral flatness measure 0.97) and lowest sidelobes (PSR = −21.4 dB), it is perfectly periodic (IPCG = 1.0) and therefore fully exploitable by a replica-based interceptor. Lorenz-CBFM reduces the IPCG to 0.072, essentially the noise-radar floor (0.063), while delivering a thumbtack ambiguity function free of FMCW’s range–Doppler coupling, at the cost of modestly higher sidelobes (−17.8 dB). A derivation linking IPCG to interceptor coherent gain shows that a replica-reuse interceptor detects an FMCW emitter from about 14 times farther away than a Lorenz-CBFM emitter. A convolutional-neural-network experiment confirms that all four families are recognizable by type, yet a learned next-pulse predictor recovers near-unity coherent gain only for FMCW. Detection is modulation-independent at equal pulse energy, while the thumbtack waveforms remove a systematic range–Doppler bias that displaces a 1500 m/s FMCW target by a full range-resolution cell. A 13-point parameter study identifies the Lorenz parameter ranges maximizing spectral flatness and minimizing sidelobe levels.