A ring of three unidirectionally coupled semiconductor lasers (RTUC-SLs) is used to generate broadband chaos with no pronounced time-delay (TD) signature. Using the autocorrelation function and permutation entropy as the TD measures, we demonstrate that under suitable coupling strength, the loss of the TD signature of the lasers in the RTUC-SL configuration is achieved both for the intensity and the phase. These findings should prove valuable for developing high-quality optical chaos for potential applications, such as chaos-based communications and random number generation.