This is a poor chapter break. This could be a good time to remind everyone that the Bible was not written with chapter divisions. They were added later to helps us better find passages (It is easier to say Isaiah 43:2, then say Isaiah said. I mean should we really be expected to know where Isaiah might have said something). I say that because 3:1-10 continues the thought of the end of chapter 2, which is Paul’s concern for their spiritual well-being.
Specifically, Paul is worried about their faith (notice the repetition of your faith in this section). Paul’s concern leads him to send Timothy (what trust Paul had in this young man). He wants to ensure that his missionary efforts were not in vain (compare 2:1 with 3:5, so far the work of Paul had not been in vain, but that could all change).