Each Squaddie has two slots for Chemistry.

The first is the Active slot. Any Chemistry here is never lost.
The second is the New Potential slot. You can move a Chemistry here to the Active slot, but you lose the existing Active slot Chemistry, if any. This slot is cleared whenever the Squad goes on a mission, I think. I'm not 100% sure on cases where the Squaddie in question is left behind.

To actually move a Chemistry from the Potential to the Active slot, you go through the Roster on the wall.