Ok, I did some more testing with a chain of two Chain events and I was able to reproduce the bug. But: I think I've also found out what's the problem.
Apparently it's got nothing to do with the position of the Chain event (it's okay to begin a chain with a Chain event), but DC seems to automatically transfer the event conditions you set for one Chain event to the next event in line, which is probably the cause your chain was broken. Check all the conditions on every single event and correct them if they don't make sense, that should do the trick.
I'm not sure if it's a bug or a design choice but I think it's safer to insure "Always" is the default event condition for each and every event, regardless of its predecessors.
Edit:
To make things a little clearer, what's causing problems here is not the event condition per se but the second part of it. If you've got a Chain event that fires when Quest 1 is completed, the chained event will have the same condition "If quest is completed" (and that's ok, even though it's quite futile) but the quest will not be selected (no quest, instead of Quest 1). Therefor the conditions ("If quest is completed" - no quest) will not be met.