Once you've researched Alien Alloys, you will be able to research Personal Armour.
Tactically, Personal Armour can be useful, as it gives soldiers slightly better chances of surviving being shot. However, from a bean-counter's point of view, it's not very efficient, as alien plasma weapons will frequently kill your soldiers despite the armour and the (expensive) armour suit is then lost along with the soldier. If you're expecting a mission to be very difficult (e.g. Sectoid Terror Mission), it may be worth bringing a few suits of Personal Armour along; otherwise, your wallet will thank you for your callousness in sending soldiers into battle without armour.
Sell Value: $54,000
Due to a bug when units are spawned, soldiers wearing Personal Armour are treated as though they are wearing Power Armor when damage modifiers are applied -- but a Power Suit or better is needed against stun damage from smoke.