The Greek text of Jοhn 1:3 states,
Γʹ πάντα δι᾽ αὐτοῦ ἐγένετο καὶ χωρὶς αὐτοῦ ἐγένετο οὐδὲ ἕν ὃ γέγονεν
which may be translated into English as,
3 Everything was made by means of him, and without him, not even one thing that was made was made.
First, we note that «πάντα δι᾽ αὐτοῦ ἐγένετο» (1:3a) is parallel to «ὁ κόσμος δι᾽ αὐτοῦ ἐγένετο» (“the world was made by means of him”) (1:10b). Thus, πάντα, being equivalent to ὁ κόσμος, represents absolutely everything created. In the first clause, the author states that absolutely everything (i.e., everything created) came into existence (“was made”) by means of the Word. This precludes the Word from being a creation, for the Word that (hypothetically) did not yet exist could not have created itself.
The second clause emphasizes the first clause and absolutely precludes the possibility that there was something made that was not made (i.e., came into existence, created) by means of the Word.
The preposition χωρίς is commonly followed by a substantive (i.e., pronoun, noun) declined in the genitive and means “absent” in the sense of “in the absence of; without.”1 For example, «χωρὶς ἡμῶν ἐβασιλεύσατε»—“You reigned without us.”2 The preposition χωρίς can also mean “besides” (as in “excluding, except”), but such a translation would be nonsensical in John 1:3:
3 Everything was made by means of him, and besides him, not even one thing that was made was made.
In order for the Arian belief to be derived from John 1:3, we might expect the Greek text to have stated,
Γʹ οὗτος μόνος ὑπὸ τοῦ θεοῦ ἐγένετο καὶ τὰ ἑτέρα διὰ τούτου ἐγένετο.
which may be translated into English as,
3 He alone was made by God, and the other things were made by means of him.
In summary, χωρὶς αὐτοῦ in John 1:3b emphasizes that the Word is not reckoned among the creation. That is, the Word is the Creator. It in no way supports the Arian belief that the Word was the first thing created by which everything else was created.
References
Wilke, Christian Gottlob. A Greek-English Lexicon of the New Testament: Being Grimm Wilke’s Clavis Novi Testamenti. Trans. Thayer, Joseph Henry.Ed. Grimm, Carl Ludwig Wilibald. Rev. ed. New York: American Book, 1889.
Footnotes
1 Thayer, p. 675, χωρὶς, 2
2 1 Cor. 4:8
3 Thayer, p. 675, χωρὶς, 3; cp. Matt. 14:21, 15:38; 2 Cor. 11:28