In order to reduce the load on the user's machine, Chrome limits alarms to at most once every 1 minute but may delay them an arbitrary amount more. That is, setting delayInMinutes or periodInMinutes to less than 1 will not be honored and will cause a warning. when can be set to less than 1 minute after "now" without warning but won't actually cause the alarm to fire for at least 1 minute.
To help you debug your app or extension, when you've loaded it unpacked, there's no limit to how often the alarm can fire.