What causes chicken to feel rubbery?

I grill out often during the summer. I’ve grilled boneless skinless chicken breast many times, but a few times I have been puzzled about the texture of the chicken. “Rubbery” is the best way I can describe it. Even before I cook it, I can tell that there is something different. The meat seems to separate in strands. I know that muscle is made up of strands, but this is different. The meat breaks up (after cooked) in groups of strands – if that makes sense. When you bite into it it is not tender, but rubbery.