There certainly is such a function! You can change three different background colours on the chart by getting the ChartStyle object from the ShinobiChart (using the getStyle() method), calling the relevant method and finally calling redrawChart() on the ShinobiChart.
The three background colours are as follows:
setPlotAreaBackgroundColor(int) - this is the area where the series are drawn, in your picture above it's the grey area
setCanvasBackgroundColor(int) - this is the area taken up by the plot area plus the axes
setBackgroundColor(int) - this is the area taken up by the canvas area plus the chart's title and the legend if it is shown and is outside the plot area
Note that the plot area sits on top of the canvas, which in turn sits on top of the chart.
Hope that helps!