My chest display isn't a circuit board, it's an iPod...but it illustrates my suggestion for the approach.

Full WIP:
http://mandalorianmercs.org/forum/index.php?topic=93907.165I'd avoid gluing it permanently in, instead I'd suggest building a Sintra frame that fits around the board and gluing that in back of the plate. Then you know the board will have a custom-shaped slot to fit in and won't wobble out.
Then, depending upon the board's specific layout and dimensions, you could do anything from simply securing it with gaffer tape, make some strips of Sintra that go across the board and screw into the frame or maybe make some tabs out of Sintra that are attached with a screw to the frame and then rotate around to hold the board.
If you can make a shaped frame that the board slots into, then some kind of easy to remove fixing you'll be able to reuse the display on any upgraded plates, repair/remove it if anything fails.
Because of the curve of your chest plate and the softness of your vest/flight suit you have more space under there than you might think!
Hope that helps