When you use the attack action, you can make one attack at your highest base attack bonus that deals additional damage. Roll the weapon’s damage dice for the attack twice and add the results together before adding bonuses from Strength, weapon abilities (such as flaming), precision-based damage, and other damage bonuses. These extra weapon damage dice are not multiplied on a critical hit, but are added to the total.
At 3rd level, when a two-handed fighter makes a single attack (with the attack action or a charge) with a two-handed weapon, he adds double his Strength bonus on damage rolls.
This ability replaces Armor Training 1.
So my understanding is that they both modify the same action, but different parts, thus allowing stacking. Vital Strike modifies the weapon damage dice, while Overhand Chop modifies the Strength bonus at the end of the damage dice being rolled. I have heard from different sources that Vital Strike and Overhand Chop can't be combined. Some say that one action can only be modified once. Other sources say that the two effects can't be combined because Vital Strike is a special attack. Any ideas on which is right?
As far as I can read the rules, they do stack by RAW.
The key points are the following statements:
Since they both call to the "Attack Action", and the Vital Strike specifies that it is a single attack. All prerequisites for Overhand Chop are fulfilled.
In fact, even if they both changed the damage die they would stack. Unless one (or both) specifically prohibited this.