This work proposes a systematic approach for constructing discrete chaotic systems from chirp signals and illustrates it through two representative maps. Detailed analysis shows that the resulting systems exhibit complex dynamics, including crises, period-doubling transitions to chaos, and, in some regimes, robust chaos. With multiple control parameters and high Lyapunov exponents, the maps demonstrate strong sensitivity to initial conditions, as confirmed through bifurcation diagrams and Lyapunov exponent plots. The maps are integrated into a pseudo-random bit generator (PRBG) to evaluate their statistical suitability, and both pass all tests of the NIST Statistical Test Suite. Additional evaluations include key-space estimation, operation-based computational complexity, and execution speed measurements. The results indicate that the proposed chirp-based maps are effective candidates for chaotic PRBG design and related applications.