The other answers didn’t work for me. I found the answer in their documentation:
http://api.highcharts.com/highcharts#Series
Using this method (see JSFiddle example):
var chart = new Highcharts.Chart({
chart: {
renderTo: 'container'
},
series: [{
data: [29.9, 71.5, 106.4, 129.2, 144.0, 176.0, 135.6, 148.5, 216.4, 194.1, 95.6, 54.4]
}]
});
// the button action
$('#button').click(function() {
chart.series[0].setData([129.2, 144.0, 176.0, 135.6, 148.5, 216.4, 194.1, 95.6, 54.4, 29.9, 71.5, 106.4] );
});