Does deathtouch on a creature with first strike kill the blocker before second strike damage is dealt?

First strike causes a creature to deal its combat damage in a special first combat damage step that occurs before the normal combat damage step (CR 702.7b). Deathtouch means that any amount of damage dealt by the creature is considered lethal damage (CR 702.2b). These two abilities combine very powerfully.

When a creature with both first strike and deathtouch deals even 1 point of damage to a blocker in the first combat damage step, that damage is considered lethal. State-based actions are then checked after that step (CR 704.3), and any creature that has been dealt lethal damage is destroyed at that point — before the second combat damage step ever happens.

This means the blocker is destroyed before it gets a chance to deal damage back in the normal combat damage step, effectively giving the attacking creature a way to kill the blocker without receiving any damage in return (assuming the blocker does not also have first strike or double strike).

Example: Your 1/1 creature with first strike and deathtouch attacks. Your opponent blocks with a 5/5. In the first combat damage step, your 1/1 deals 1 damage to the 5/5. Because of deathtouch, that 1 damage is lethal. State-based actions destroy the 5/5. The second combat damage step occurs, but the 5/5 is already gone and deals no damage to your creature.

Note: if the blocker also has first strike or double strike, both creatures deal damage simultaneously in the first combat damage step (CR 702.7b), and the blocker's damage is also dealt at that time — so your creature may still die.