In his Homilies on the Gospel of John, John Chrysostom (347-407 AD) writes the following regarding John 17:3:
John Chrysostom - Homily 80 on the Gospel of John
"And this is life eternal, that they might know You the only true God, and Jesus Christ whom You have sent."
The only true God, He says, by way of distinction from those which are not gods; for He was about to send them to the Gentiles. But if they will not allow this, but on account of this word only reject the Son from being true God, in this way as they proceed they reject Him from being God at all. For He also says, "You seek not the glory which is from the only God" (John 5:44). Well then; shall not the Son be God? But if the Son be God, and the Son of the Father who is called the Only God, it is clear that He also is true, and the Son of Him who is called the Only true God. Why, when Paul says, "Or I only and Barnabas" (1 Corinthians 9:6), does he exclude Barnabas? Not at all; for the only is put by way of distinction from others. And, if He be not true God, how is He Truth? For truth far surpasses what is true. What shall we call the not being a true man, tell me? Shall we not call it the not being a man at all? So if the Son is not true God, how is He God? And how makes He us gods and sons, if He is not true? But on these matters we have spoken more particularly in another place; wherefore let us apply ourselves to what follows.
Above, John Chrysostom argues that Jesus calling the Father "the only true God" does not exclude Himself from being God, and cites 1 Corinthians 9:6 to demonstrate his point, which says, "Or is it only Barnabas and I who have no right to refrain from working for a living". John Chrysostom apparently argues that the verse should say something like, "only I, (and also Barnabas)", showing that Paul's "only" does not exclude all others, but his point is unclear, and it appears that he is using an overly-wooden translation of the passage, when in reality, the "only" is actually supposed to be applied to both Paul and Barnabas in 1 Corinthians 9:6.
Therefore, 1 Corinthians 9:6 would not be a good counterpoint to the Unitarian understanding of John 17:3. The Apostle Paul is not distinguishing himself from Barnabas, and yet still including him. He is simply saying that he and Barnabas are being singled out from a group.
For a discussion of a better objection of this type, see this article, which discusses John 17:3 in light of Jude 1:4.
John Chrysostom then says, referring to Jesus, "And, if He be not true God, how is He Truth? For truth far surpasses what is true", apparently referring to Jesus calling Himself "the truth" (John 14:6). However, it does not follow that Jesus being called "the truth" means that He is "the true God". That argument is simply a non sequitur. Jesus can be "the truth" in that He brings what is true, and speaks what is true, and in many other ways that do not really have anything to do with whether or not He is God.
John Chrysostom then says, "And how makes He us gods and sons, if He is not true?". This argument is, again, very raw, and unconvincing. There is no reason to think that Jesus making us sons of God means that He must be God, because such a situation can be arranged by God, who is over Jesus, and can empower Him, or decree that all who believe in Him become His sons, and so on.
John Chrysostom acknowledges that in John 17:3, the Father is called "the only true God" "by way of distinction from those which are not gods". However, he downplays the fact that in the verse, Jesus explicitly distinguishes Himself from "the only true God", and refers to Himself as a separate subject "sent" by Him. Because Jesus designates the Father specifically as "the only true God", in distinction from Himself, then that means that there are none others, including Himself, who are "the only true God".