You can check the logs.. syslog, kern.log, dmesg in /var/log (default location) for errors. I would start there.
In addition to the system logs, I would also enable/increase the Chef-Client logging in the config file for the client. From Chef-Docs you can enable Verbose logging and/or change the log_location to a file on the system for you to review.
The combination of the system & Chef logs should be a good start for troubleshooting and passing along to Chef support if needed.
As a side note, I found Chef's IRC chan to be quite helpful when I was getting started with their product.
Lastly, if those steps don't provide the information you need, you could look into using https://wiki.ubuntu.com/DebuggingProgramCrash or https://wiki.ubuntu.com/Kernel/KernelDebuggingTricks to help gather data.