This article covers the compatibility of Google Chrome OS to Trend Micro Endpoint Security Products
Currently, Chrome OS does not support Trend Micro Apex One or Worry-Free Business Security Products (Both On-premise and SaaS versions), as the operating system is based on Linux Kernel and was designed to behave similarly to a desktop version of Android, thus the windows installation file (.exe) cannot be executed.
Another reason why the Trend Micro Mobile Security can be installed on chromeOS is due to Google allowing porting of apps from Android to chromebook. Since the TMMS agent is published on Play Store and chromeOS does allow installation of .apk, then it is possible to deploy the agent on those devices. However it is not listed on system requirements.
We would recommend to use the Trend Micro Mobile Security for Enterprise as the is partially supported. However there will be some additional functionalities that may be limited or not applicable to Chrome OS but works well with the Android Operating System such as App Lock.