A new two-dimensional chaotic system, called the Cubic Trigonometric Coupled Map (CTCM), is proposed in this article. It is characterised by strong nonlinear interactions and complex dynamic behaviour. A thorough review of the Lyapunov exponents and bifurcation structures shows that CTCM has a strange attractor with fractal geometry and is highly sensitive to initial conditions. In addition, a new pseudo-random number generator (PRNG) based on the chaotic characteristics of the CTCM has been implemented. Experimental results show that the generator achieves near-optimal entropy levels up to 7.999 with high sensitivity to initial conditions, making this PRNG a promising solution for applications in information security, numerical modeling, stochastic simulations, data encryption, and secure communication systems.