Hey, look at that! Chain starting a chain works for me.

(It hadn't before, but I suspect it was because of my coupling with a Logic Block event that I must have done something wrong in).
I think that JonnieR may be using Chain because it is easier to keep track visually of what is going on in the event chain.
While JonnieR's and my attempts may contradict, I assure that mine worked.

I've tested with the following four chains and conditions:
Starting positions 0,0 facing East
chain #1 at 1,0
-Text Statement
--chain (if facing West)
---normal chain = Text Statement
---chained event = Text statement
chain #2 at 3,0
-Text Statement
--chain (if facing East)
---normal chain = Text Statement
---chained event = Text statement
chain #3 at 5,0
-chain (if facing West)
--normal chain = Text Statement
--chained event = Text statement
chain #4 at 7,0
-chain (if facing East)
--normal chain = Text Statement
--chained event = Text statement
In each of the cases, the Text Statement in each of the chans states what it is, i.e. "This is the normal chain." and "This is the chained event."
Simply start at the starting point and head East.