Chain skip happening seemingly at random with a new chain My bike's a 24-gear trail/road hybrid, and I've had it for about three years (although I've been riding it much more lately than in previous years).

For a long while, I've had an issue with chain skip happening seemingly at random, even on level, paved paths, however this issue was always more serious going uphill. I decided to replace my chain yesterday (it's appropriately sized, was pre-lubed, and none of the links locked upon inspection), however on this morning's commute I still got the same amount of skip, likewise more serious going uphill.

I've tried using best practices to avoid this issue, as well:


I avoid pedalling while changing gears
I've checked my front and rear derailleur alignment (and adjusted it as best I could, there's still a very, very slight amount of scraping on the front derailleur if the chain has to travel too far laterally e.g. between my largest front sprocket and the smallest sprocket on the cassette on the rear wheel)
I've double-checked that the links don't block, multiple times
The teeth on the front sprockets as well as on the cassette don't seem to be overly worn down


Two more factors could be relevant to this; this new chain has those "tool-free" break links (you bend the chain to attach or detach one side of the link and break the chain), and I'm a more heavyset guy, so I pedal hard - I think this could be putting more stress on the chain.

I'm not sure what else I can do to reduce chain skip.

Update: I've gone by my LBS and apparently one of the chain gears is in fact worn down (I just didn't know how to tell, apparently).
Pedaling while changing gears in important to avoid damage to derailleur and chain.  Gear shifting proper technique by Sheldon Brown.
Shift the gears so that chain is on the middle chain ring(at the pedals) and approximately on the middle gear on the cassette. Verify that the derailer with the chain is vertical, if not adjust accordingly. 
Also, it is possible that chain may be skipping if the derailleur is slightly bent - in this case bring your bike in to a reputed local bike shop(LBS) and have it checked out. It may save your derailleur from further damage and possible need to replace it.
Changing to an easier gear just before you climb and spinning pedals (lower effort but slightly higher pedal cadence), instead of mashing on a tougher gear (applying greater force and lower pedal cadence) helps avoid chain skipping.