Pseudorandom number generators (PRNGs) generate random bit streams based on deterministic algorithms. Any bit stream generated with a PRNG will repeat itself at a certain point, and the bit streams will become correlated. As a result, all bit streams generated in this manner are statistically weak. Such weakness leads to a strong connection between PRNGs and chaos, which is characterized by ergodicity, confusion, complexity, sensitivity to initial conditions, and dependence on control parameters. In this study, we introduce a PRNG that generates bit sequences by sampling two Arnold cat map outputs. The statistical randomness of bit streams obtained using this PRNG was verified by statistical analyses such as the NIST test suite, the scale index method, statistical complexity measures, and autocorrelation. The generated bit streams successfully passed all the analytical tests and can be safely used for the many applications of randomness.