I have a stepper motor driven by an Allegro A4983 stepper driver chip and in some cases the motor can be back driven even while being powered up. This leads to blown motor driver chips.
Would I be able to use a pair of zener diodes placed in opposite directions between the A+ and A-, B+ and B- coils to to clip high voltages when the motors are back driven to protect my motor driver from being fried or is there another solution to this?
Yes. Back to back series zeners will work OK. Ensure voltage rating of any one zener is at least slightly greater than maximum voltage that will occur across windings. Note that if you have a centre tapped winding (or motor coil) and the CT is connected to V+ and you ground one end, the other end will rise to +2V+ - so using clamp diodes direct to 1 x V+ will badly affect motor operation.
Another solution is diode from each motor terminal to a voltage sink that is slightly higher than the allowed maximum voltage in normal use. The sink may be a formal power supply with enough load to absorb the spikes or a common zener or clamp regulator which is diode connected from each winding.
You may have to implement a below ground clamp as well depending on circuitry.