The issue here is not the refreezing after cooking, but rather the method of initial thawing.
Thawing methods should ensure that food does not enter and stay in the danger zone (40 F - 140 F, 40 C) for any longer than absolutely necessary, and certainly not for time measured in hours. Doing so risks the growth of pathogens and resultant foodborn illness.
Thawing foods by leaving them out at room temperature—especially, for example, while you go to work—is not a good idea for a couple of reasons. The food on the outside may be too warm before the center is thawed; and if not monitored, there is no way to know when it about to enter unsafe temperatures.
The recommended methods of thawing are:
- In the refrigerator
- As part of the cooking process
- Under flowing cool water
- In the microwave
One or more of these may be appropriate depending on the food item and how it will be prepared.
You should use one of these methods to thaw your chicken.
Assuming that food has been treated safely throughout its lifetime including during thawing, there is no safety reason why it cannot be refrozen. This may reduce quality and affect texture, but it is not a safety issue.