Is "either ... or ... or" used properly used in the following?
When something bad happens, you have three choices. You can either let it define you, or let it destroy you, or you can let it strengthen you.
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According to Merriam-Webster, definition #3, "either" is ... "—used as a function word before two or more coordinate words, phrases, or clauses joined usually by or to indicate that what immediately follows is the first of two or more alternatives"
Since they say, "two or more", your sentence is fine.
Definitions 1 and 2 of the same entry specify only 2 alternatives:
def. 1 "being the one and the other of two" //flowers blooming on either side of the walk
def. 2 "being the one or the other of two" //take either road
But those definitions seem to apply to cases where you don't list the different options. It's OK to say "either A, or B, or C".