1/35th inch is 0.02875"; 3' is 0.08571" Dividing that into 1 inch--a common unit of fine chain measure, that's 11.66 links per inch. You could probably use 15 link-per-inch chain.
Check with the model ship suppliers, they have resin chain in oval shape, with stud links like heavy chain ought to,
As to line, 1.5 diameter line scales to 0.04286, a bit larger than 1/16" (it's right at 3/64" if you really need to know).
Looking at my wire gauge chart, 18 AWG twisted wire would suit--and not have any fuzz like thread would have.
Now, in some fairness, your question double-clutched me a bit. See, naval chain is "wire sized" meaning the effective thickness of the material bent to make the link, not the overall size of the link. So, 3" chain would have links around 9" wide and a foot long--destroyer anchor chain--and would be 2-3 links per inch at 1/35.
Further, in the days before mantled rope, the line was made up from strands, then ropes, then hawsers and then into cables, making them very had to size by diameter. So, they were sized by circumference. So, a 1.5" line in the days of sail was only about 0.477" in diameter. Which is a very fine 0.01364" (smaller than 40 gauge wire) in 1/35 scale.