Nope for chain
As far as titanium chain mail stopping a bullet, probably not. First, titanium has lower strengths-per-volume compared to steel. This will mean that a titanium chain mail armor is weaker than a steel chain mail, and use of steel chain mail in the 1800s as protection against bullets did not work out well. (The titanium chain mail must be weaker in order to allow for the same flexibility as the steel one.) In addition, titanium is generally more brittle than steel, so the rings would shatter and actually make the problem worse.
Not worth it for plate
A titanium plate would work better, but it would be thicker than an equivalent steel plate. While it would be lighter it would also be bulkier, making the joints even larger, and possible cumbersome. In addition, because titanium is more brittle it would be more likely to crack from a shot as opposed warping and retaining most of the strength.
In addition, because the titanium is more likely to be cracked than warped, you can't just hammer out dents in it in the field. The difficulty in working titanium (it requires an inert atmosphere and not many people know how to work it) is actually a significant amount of the cost. Meanwhile getting people to work steel is easy.