Hi,I'm Miranda, and I'll be happy to help you with your question.
Your chicken noodle soup should be just fine. Soup left out for extended periods of time without refrigeration can accumulate a large amount of bacteria, such as Clostridium perfringens, Clostridium botulinum, Bacillus cereus, etc. However, since it was just left out overnight, the best thing to do is reboil it for 10 minutes (and keep it at a full boil), then put it in the refrigerator this morning. It hasn't been cool long enough for the bacteria to germinate and reproduce up to dangerous levels, so boiling and refrigerating this morning will do the job just fine.
Here is an article that provides more information: http://www.thekitchn.com/soup-left-out-overnight-is-it-still-safe-to-eat-178685
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After remembering, I just threw it in the fridge... if I boil it now, could it be eaten or no? I'm mainly concerned about the chicken.
It should be fine. Go ahead and boil it (at a full boil) for a good 10 minutes just to be safe. The chicken won't be a problem.