This would be a great addition, considering the time input is reformatted to full 4-digit 24hr time despite the field only allowing 2 digits.
If you're going to add minutes, go ahead and go all the way and don't do it by fractions.
I don't believe making this more complex is really necessary. You can do minutes by adding an extra timeline that drills down to the sections where you need this accuracy and simply assume that the hours / days / months are whatever unit you need.
I'd really like to see this. One of the events I'd like to make a timeline for is a skirmish that took just a few hours, where individual actions in isolation combined to make it a disaster on both sides. A timeline is actually the best way I've found to make it emotionally impactful, since there's not much room for editorializing and it gives a top-down view of everything collapsing at once.
Something to consider for Chronos. Zoomed in timelines totally have a possibility of multiple things happening within the hour then the need to sort them by minutes will arise.