Counter Strike

If I play Counter Strike in response to my opponent's Elder Dragon's play effect, will the chosen unit still die?

No, the unit protected by Counter Strike will not die.

Elder Dragon's passive ability changes the definition for what is considered lethal damage for a unit, as long as that unit has damage marked by Elder Dragon's controller on it. However, this doesn't change the actual amount of damage being dealt. Elder Dragon deals 1 damage to up to one unit at each location-if one of those units has a prevent effect applied to it, that prevent effect will replace as much of that damage as it can. In the case of Counter Strike, it will replace all of the damage. If the damage is entirely prevented, it is never dealt per rule 437.2.a., and thus there is no opportunity for the passive ability of Elder Dragon to apply to that unit.

437.2.a.The damage being dealt as a result of Preventing can never be less than 0, but can be 0. This is equivalent to not dealing damage.

467.2.c.10. If a unit cannot be dealt damage, then no amount of damage can be considered lethal. Such a unit is exempt from any considerations of mandatory assignment. Example: Kayn, Unleashed says "If I have moved twice this turn, I don't take damage." While Kayn can't take damage, it is ignored for the purposes of assigning lethal damage in combat. Example: Counter Strike says "Choose a unit. The next time that unit would be dealt damage this turn, prevent it." The unit in question has a replacement effect applied to it, but it still can be dealt damage. Thus, it is not exempt from considerations of mandatory assignment.