Can you counter a triggered ability that triggers when a permanent enters the battlefield?

Triggered abilities are not spells — they are abilities that go on the stack separately from the permanent that caused them. When a permanent enters the battlefield and its triggered ability triggers, that ability is placed on the stack and players receive priority. At that point, any spell or effect that can counter a triggered ability (such as Stifle or Disallow) can be used to counter it. (CR 603.1, 603.3)

It's important to note that countering the triggered ability does NOT counter or remove the permanent itself. The permanent is already on the battlefield. Only the ability is countered. (CR 603.6)

Standard counterspells like Counterspell or Cancel only counter spells (CR 700.2), so they cannot counter a triggered ability. You need a spell or ability that specifically says it counters a target activated or triggered ability.

Concrete example: Your opponent plays Elvish Visionary, which has a triggered ability "When Elvish Visionary enters the battlefield, draw a card." That trigger goes on the stack. You respond by casting Stifle, targeting the triggered ability. The trigger is countered, your opponent does not draw a card, but Elvish Visionary remains on the battlefield.

In summary: yes, you can counter an enters-the-battlefield triggered ability as long as you have a spell or ability that specifically counters triggered abilities. The permanent itself is unaffected. (CR 603.1, 603.3, 603.6)