You can do this by using the power of setTimeout() method. This allows you set a timer to trigger a function call in the future, and calling it won't block execution of the current / other functions.

First, Position a div containing the spinner above the chart image, with it's css display attribute set to none:

<div>&nbsp;<img src="spinner.gif" id="spinnerImg" style="display: none;" /></div>

The nbsp stop the div collapsing when the spinner is hidden.

function chartOnClick() {
  //How long to show the spinner for in ms (eg 3 seconds)
  var spinnerShowTime = 3000

  //Show the spinner
  document.getElementById('spinnerImg').style.display = "";

  //Change the chart src
  document.getElementById('chart').src = '/charts/10.png';

  //Set the timeout on the spinner
  setTimeout("hideSpinner()", spinnerShowTime);
}

function hideSpinner() {
  document.getElementById('spinnerImg').style.display = "none";
}