Can I RE-freeze chicken soup after it has thawed?
Yes, you can, assuming that the total time the soup (which is very perishable) has spent in the danger zone (40 F to 140 F, 4 C to 60 C) is less than 2 hours for the entire lifetime of the soup and its ingredients, from raw, and through all of the cooking, heating and cooling cycles.

If you have boiled the soup after thawing it, any new pathogens will have been killed.  The conservative recommendation above is because some pathogens leave behind toxins that are not destroyed by simple boiling.  In practice, these recommendations may be extremely conservative, but you will have to assess your own risk tolerance.

Of course, the quality of the soup, especially if it has noodles or potatoes, may suffer during the heating and cooling cycles.

See:  How do I know if food left at room temperature is still safe to eat?