Believe it or not, this was not an oversight. When I designed the nested exception facility I thought carefully about which excpeptions should be given a (Throwable) constructor, and came to the conclusion that IllegalArgumentException did not need one, even though it is designed to be extended. The rationale is that this constructor is designed specifically for use when an input parameter is invalid, not when some lower-level action fails (throwing an exception that demands nesting). I understand that it's theoretically possible that such an exception is the direct result on an invalid parameter, but it appears impractical for a program to make that determination.
When the chained excption facility was designed, I was unable to come up with a situation wherein a program would actually want to throw an IllegalArgumentException with a nested Exception. I am marking this exception incomplete to give the reporter an opportunity to describe such an scenario. Barring such a scenario, I believe this bug should be closed.