I’m playing Storm King’s Thunder in Dungeons & Dragons 5th edition. I have a Paladin who has taken the Oath of Vengeance (PHB, p. 87-88). With that oath, I get my Channel Divinity options and spells like hunter’s mark and shield.
During combat in the game I cast the spell hunter’s mark on the enemy as a bonus action on my first turn. The second turn of combat I invoked my Vow of Enmity as a bonus action which is a Channel Divinity option available to a vengeance paladin. The DM’s response was that I can’t do that. He said it would require my concentration and thus break hunter’s mark.
Vow of Enmity
Vow of Enmity is a Channel Divinity option available to a Paladin who has taken the Oath of Vengeance:
Vow of Enmity. As a bonus action, you can utter a vow of enmity against a creature you can see within 10 feet of you, using your Channel Divinity. You gain advantage on attack rolls against the creature for 1 minute or until it drops to 0 hit points or falls unconscious.
Hunter’s Mark
Hunter’s mark is an oath spell for a Paladin who has taken the Oath of Vengeance. Its description in the PHB clearly states that it requires concentration.
You choose a creature you can see within range and mystically mark it as your quarry. Until the spell ends, you deal an extra 1d6 damage to the target whenever you hit it with a weapon attack, and you have advantage on any Wisdom (Perception) or Wisdom (Survival) check you make to find it. If the target drops to 0 hit points before this spell ends, you can use a bonus action on a subsequent turn of yours to mark a new creature.
At Higher Levels. When you cast this spell using a spell slot of 3rd or 4th level, you can maintain your concentration on the spell for up to 8 hours. When you use a spell slot of 5th level or higher, you can maintain your concentration on the spell for up to 24 hours.
According to an unofficial tweet by Jeremy Crawford from September 2015, Channel Divinity options are not spells.
The following StackExchange question discusses whether using a Channel Divinity option ends the sanctuary spell: Does Channel Divinity / Turn Undead break sanctuary?
Based on the description of the Channel Divinity option Vow of Enmity and other info as described, I feel that I can infer that Vow of Enmity does not specifically require concentration.
Does using a Channel Divinity option require concentration?
My DM said that using a Channel Divinity option would require concentration, and so I chose to drop hunter’s mark. I missed the attack with advantage. Then the giant was killed by the other adventurers in my party before I could do anything. I felt like my DM was inflexible with the RAW Channel Divinity option.
Channel Divinity
The description of Channel Divinity options in the Sacred Oath feature says:
Your oath allows you to channel divine energy to fuel magical effects. Each Channel Divinity option provided by your oath explains how to use it.
When you use your Channel Divinity, you choose which option to use. You must then finish a short or long rest to use your Channel Divinity again.
This isn’t a game-breaking mechanic, considering that a Paladin can only activate the Vow of Enmity against one creature per rest. I roleplayed performing the Vow of Enmity, and I felt penalized for my choice because of the DM’s ruling.
Vow of Enmity does not require concentration
Nowhere in the description of a paladin’s Channel Divinity (PHB, p. 85) or the Vow of Enmity option (PHB, p. 88) does it mention that it requires concentration, so it doesn’t. Using the ability simply activates it, and it does not require concentration to maintain.
Concentration is a rule that usually applies to spells, as detailed on page 203 of the PHB under it’s own section. Other features that “hijack” the concentration rule make reference to spells, using wording such as “as if you were concentrating on a spell”1. In other words, if a feature is meant to include concentration, it explicitly says so.
RAW, using this option would not have affected your concentration on the hunter’s mark spell.
1 As an example of this wording, stealing from this related question, an example of a cleric’s Channel Divinity option, specifically the Trickery Domain cleric’s Invoke Duplicity ability:
As an action, you create a perfect illusion of yourself that lasts for 1 minute, or until you lose your concentration (as if you were concentrating on a spell).
Hence this example would interfere with concentrating on a spell, but only because it explicitly says that it uses the concentration rule.