Digital chaotic sequence spread spectrum (CSSS) communication systems provide a number of advantages for secure communications due to the apparent bandlimited Gaussian noise-like signal characteristics and the non-repeating nature of the underlying chipping sequence. The Rayleigh magnitude distribution of the signal represents a challenge, however, for transmission through linear highpower amplifiers (HPA), both due to the high peak-to-average power ratio (PAPR) and the impacts of selective signal compression on the tails of the time-domain Gaussian signals, which becomes observable by cyclostationary low probability of detection (LPD) metrics. This paper first provides an analysis of HPA compression effects on a single-carrier CSSS signal to understand the HPA-induced artifacts when pushed into compression. This work also defines and evaluates time-domain pre-distortion techniques for memoryless HPAs, validating those formulations through Matlab simulations and live measurements of predistorted CSSS signals transmitted through physical HPAs. Unlike computationally expensive statistical models used to predistort multi-carrier waveforms, this technique is shown to be a computationally efficient method to minimize the increased likelihood of adversarial detection of single-carrier waveforms. The proposed pre-distortion techniques are measured as achieving an average of 3.35 dB in improvements for linear operating range, enabling transmission of CSSS waveforms at an HPA backoff of 4.80 dB without adversely affecting kurtosis-based signal detectability.