Thanks to all for the helpful replies. I have not yet called UA to rebook the LAX-ORD connection (hopefully without penalty) but will do so later this week.

FYI, looking at the Air New Zealand schedule page, (this is mainly aimed at Chapel Hill Guy) the Sunday CHC-LAX flight has changed from an 8:00pm departure to a 9:25pm departure. The Tuesday flight remains at 8:00.

http://timetables.oag.com/nz/