The saying is: Christ Jesus came into the world to save sinners. Paul adds that he is the foremost (or chief) of sinners as an example of Christ’s patience. See 1 Timothy 1:15–16.
In 1 Timothy 1:15–17 Paul offers a short, memorable statement he calls “trustworthy,” centered on Christ Jesus coming into the world to rescue sinners. He then places himself as the leading example of the kind of person shown mercy, not to spotlight himself, but to show Christ’s patience in a concrete case. These verses sit within the letter’s opening push to protect and promote sound teaching and its moral results. Just before this, Paul contrasts misdirected teaching with instruction that aims at love and a good conscience, and he describes misuse of the law and the kinds of behaviors it confronts (1:3–11).
Paul treats the core statement in verses 15–16 as a repeatable summary: it is “trustworthy” and meant to be widely received. Its central explicit claim is that Christ Jesus “came into the world” with the purpose of saving sinners.
A careful answer keeps the immediate passage, the book's argument, and the whole-Bible storyline together, so the question is answered in context instead of as a detached idea.
Start with 1 Timothy 1:15-16, then read the surrounding section so the answer stays connected to the passage's flow.
15The saying is faithful, and worthy of all acceptance, that Christ Jesus came into the world to save sinners; of whom I am chief.
16However, for this cause I obtained mercy, that in me as chief, Jesus Christ might display all his patience, for an example of those who were going to believe in him to eternal life.