Seems to me that you'd want to change the chart to use a real-time search, rather than a historical search. Starting with 4.3 (and actually in 4.2.3+ if you want to change the default settings in limits.conf), you can have a real-time search backfill with historical data (e.g., if you start it up for a 1-hour window, it will fill in the past 1 hour, then start updating going forward.)
Seems to me that you'd want to change the chart to use a real-time search, rather than a historical search. Starting with 4.3 (and actually in 4.2.3+ if you want to change the default settings in limits.conf), you can have a real-time search backfill with historical data (e.g., if you start it up for a 1-hour window, it will fill in the past 1 hour, then start updating going forward.)