I've done a 1x10 on my cross bike.

There are really two options to do this:
1. Buy a 1x set up with a clutch RD and a narrow wide chainring for up front. The combination should keep the chain in place. You need the clutch RD to make the narrow-wide rings work. A regular RD can still result in a chain popping off.

2. Use a regular RD, with a bash guard and chain keeper to prevent the chain from popping off. This is the route I went. I have a regular Rival RD with a regular 42 chain, an FSA carbon bash guard and a K-Edge chain catcher.

Chain line isn't an issue really.