Why did my organic chicken come out like rubber after roasting?
It sounds like your chicken was simply overcooked.  If you used a built in pop-up timer, these almost always are set to a temperature which will overcook your poultry.

Some authorities recommend cooking white meat to 170 F (77 C), but this will leave your chicken dry and overcooked.

My personal preference is to cook white meat to about 158 F (70 C) in the oven, and then let carry over cooking bring it up a couple more degrees while it rests.  This should leave your white meat much more succulent.

Similarly, dark meat should be cooked to a temperature (to my preference) of at least 165 F (74 C) although it is much more tolerant of being overcooked.  This can be tricky when roasting a whole chicken.

Some things you can do help cook a chicken more evenly:


Cut it into parts, and roast the parts (obviously, this is ideal as each can be removed when done)
Use a high quality probe or instant read thermometer, in the thickest part of the breast or thigh, to get an accurate internal reading.   To ensure accuracy, check a couple of spots, and apply the lowest temperature.
If you don't want to fully cut it up, butterfly or "spatchcock" the chicken
Brine the chicken (although I personally prefer simply to not overcook in the first place)