Totally possible to get big hoppy flavour from no chill. There are 2 main ways I've done it in the past (both with great success).
The first, and most labour intensive is cube your wort with your 60 minute addition and don't adjust your calculations (you won't extract much more bitterness from your 60 minute addition in the cube - you can't adjust it to a 50 or 45 minute addition if you're worried, but I don't bother). Once the wort has cooled, you do a mini boil with about 5 litres of cubed wort, and add your late hops as per the recipe (10mins/flameout/etc) then chill in an ice bath in the sink. Add the cooled boiled wort to the cubed wort and ferment as usual. You can use a hop bag, or strain out the hops but I don't bother (doesn't make a difference in my experience). This is known as the Argon method (after a well regarded member).
The other option (and my preferred method these days) is to do a small bittering addition with approximately 20-30% of your IBUs, then do a massive cube hop to make up the rest of the IBUs. You'll get both bitterness and flavour, which add a great hoppy character to your beers. For example, my cube hopped APA has about 13 IBUs from centennial in the kettle, then 23 from a large cascade cube hop (ends up being around 100g of cascade). Sounds like a lot, and you do use more hops, but it works a treat. Again, i just chuck the whole lot into the fermenter and ferment as usual.
The larges cube hop i've done is around 120g in a 40L batch (split between 2 20L cubes) in an black IPA.
It doesn't take too much trial and error to nail down both methods.
I've only ever no chilled my beer, and people who are avid chillers can't tell the difference.
JD
