Definitely is a word that I saw misspelled a lot when I was teaching high school. Many students wanted to put an “a” after the “n” and spell it definately.
The funny thing is that sometimes my students’ word processors would politely offer to change the misspelled word to defiantly, which, as you can imagine, would give their sentences a whole new meaning.
Here’s the rule, then: Definitely has two i’s. If you forget the rule, think of (de)finite, which clearly uses an “i” rather than an “a.”