I listened over several times and hear 'big league'.

He says big league, but it sounds like bigly because he accents the first syllable and nearly completely swallows the /g/.

Apparently, even the BBC says There has been some speculation about whether Donald Trump said "bigly" during the US presidential debate. But I can't imagine why - I would have been prepared to believe a facetious (not ignorant, please! :) use of "bigly" until I just listened to it again, but I can't see how any native speaker could be unsure about exactly what he said there. It's plain as day he says "big league" twice. Idiomatically, "big time" would be more common, but it's just modern-day English, even in the UK.

@FumbleFingers – It's the stress pattern: he puts primary stress on big and none on league, which isn't the way most of us Americans stress it (primary stress on big and secondary stress on league). I wouldn't have expected this stress pattern to make so much difference to the way it sounds, but it does. The /g/ is audible, and I think he pronounces it as much as any other /g/ ending an unstressed syllable.

@Peter: It's very strange. I don't have brilliant hearing (I often use subtitles even for English movies), but I can't see any scope for mishearing on this one. Yet apparently many Americans find Trump's exact enunciation confusingly unclear there, and the BBC thinks it's worth a web-page, and WS2 (a competent BrE speaker) is unsure about what he heard.

@FumbleFingers Yes, 'big time' is the perfect analogous phrase. Replace when he says 'big lee...' with 'big time' and all those sentences will make sense. It is very informal though. Think of how the French say 'big blow' for 'a lot' (etymologie pour 'beaucoup')

The 'meeja' need stuff like this to keep everyone's interest. And a lot of people in the media and beyond like the idea that he might be using a non-word (pace historical usages that have been found). Has NO-ONE actually asked the man?

It's very audible. There's no mistaking it. He shortens the second syllable somewhat.

@FumbleFingers The overwhelming tide of opinion, it seems, is for big league. Perhaps the reason I did not pick that up, is that it is not a metaphor I am used to hearing. My guess is that I am not alone in that, in Britain. It was mentioned on The News Quiz tonight - where it seemed to have been heard from DT as bigly.

Jimmy Fallon heard "bigly" (in an earlier speech, not the recent debate).

I'm voting to close this question as off-topic because it is predicated on a mis-hearing.

The Language Log wrote a (actually, several) great articles on this: languagelog.ldc.upenn.edu/nll/?p=24240.

@FumbleFingers - In addition to the pronunciation confusion, I would say that the "bigly" may sound more correct. He's often using the term as an adverb, and "bigly" sounds more like an adverb than "big league". I don't know if it's different in other parts of America, but I've never heard "big league" used as an adverb, only as a noun or adjective. Thus, that confusion leads people like myself to hear "bigly", which feels better.

@FumbleFingers: Even though I know what he's saying, I hear bigly unless I'm listening for the /g/; I think because I'm used to big league having more stress on league.

@EdwinAshworth You've had a word with Donald, have you?

I'm just listening to what every comment / answer here says. The question is inappropriate on a serious website and should be deleted.

@EdwinAshworth Is that a) because DT doesn't deserve to be taken seriously? b) because expressions used by a senior politician in an English-speaking country has no bearing on current usage of the language? c) because the manner in which the language is spoken and heard, as opposed to written and read has no place here? d) because you are "an angry white man" and recoil at the thought that Donald Trump is being held up to ridicule (which was not, I might add, my motivation for asking the question).

If 'big league' is what was actually said, the question becomes genref. If 'bigly', you've answered it yourself as well as is perhaps possible. But as the jury seems to be out on what he actually said, as is stated at these articles at Language Log and Slate, then you're quite right. 'Falsely reported' is an improper close-vote reason. The correct one is 'purely opinion-based'.

@EdwinAshworth Had I not asked the question Peter Shor would not have had the opportunity to explain the phonetics of the matter.

So we now know who to thank for the computer the people at Bletchley had the opportunity to come up with. / Do we now start accepting questions about all manner of deviations in speech patterns? Allo-Alloisms? Stanley Unwinisms?