Is there a way to see where Chunks meet?

Edit: Since 1.8, the best way to do this is to hit F3 + G. This will display the chunk boundaries graphically in game. For other methods which involve coordinates, continue below.

In 1.7.x and below, if you turn on the debug display by hitting F3, you will see x:, y: and z: rows.

In the x and z rows, look at the end of each line - it shows // c: number (number) after each one. The first number is which chunk you are in, and the second is which block in that chunk, from 0 - 15.

In 1.8+, the debug screen displays the chunk coordinates differently. They are on their own line formatted as x y z in Cx, Cy, Cz, with xyz ranging from 0 to 15.

Hopefully that helps.

Note: for your specific situation, I'll add that the spawn chunks are actually a 16x16 chunk area around the world spawn point, which can be exactly determined by throwing an item into the end portal from the end - the item will appear at the exact point of the world spawn. There are other ways to find your spawn point, but if you've killed the dragon this is the easiest way.

Your redstone device should be able to occupy any chunks in that area without any problems, as they all stay loaded no matter what.

If you have the Not Enough Items mod, you can press F9 a couple times and a chunk grid will be displayed. It's nice as it's very graphical and easy to check if you are outside of the boundary.

However, you do need to have Forge and the NEI mod installed.

Screenshot I found on Imgur:

If you hit F9 again, you will get an alternate view of this which adds a grid in between the chunks, making them very visible.

You can also use the F7 key to show where mobs spawn (if you want).

Press F3 + G to show chunk boundaries.