Yes, chore is a Scrabble word!
...and is worth 10 points in Scrabble, and 10 points in Words with Friends
chore
Noun
1. A specific piece of work required to be done as a duty or for a specific fee
What Scrabble words can I make with the letters in chore?
5 Letter Words
4 Letter Words
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3 Letter Words
2 Letter Words