Rally.ui.Chart wraps an instance of a third party component which provides an Ext interface to the underlying Highchart object.
You can get a reference to that like this:
var chartWrapper = chart.down('highchart');
The code for that component lives here: https://github.com/RallySoftware/Highcharts_ExtJs_4/blob/master/Chart/ux/HighChart.js
In there you can see that it wires up a handler for window resize that calls the onResize method. Even though that's marked private I think that should work and is your best option.
chartWrapper.onResize();