TVo and I went on a leak hunt and went through the table, lines, and then opened the chiller. Opening chiller revealed a puddle under the pump (see attached picture). It looks like we have a leaky pump shaft seal. Filed WP8036 and went to swap the chiller with the spare. The spare chiller would give us a "Low Fixed Pressure" warning and would then shut down. The low threshold was set to 3.0psi and when starting the chiller it would only read around 1.4psi. No flow was ever observed while we tried to turn this on. We eventually gave up and swapped the leaky one back in.
Back in April, Greg Grabeel fixed what is currently our spare from an issue that seems to be exactly the same (alog41314). He ran the chiller in a closed loop for a week back then, so I imagine that it should work now as well. Perhaps the issue we had today was just operator error. We will look into getting parts to fix the leaky seal, and how to get the spare running again.
In an attempt to troubleshoot the spare chiller, I set it up in a closed loop and switched it on. The chiller started right up without issue and ran for ~15min without any signs of leaks.
I can't think of anything I did differently, so my current theory is that there was an air bubble trapped in an odd place. We can swap this out next Tuesday.