I had the same problem today and solved it quite easy by adding the options onAnimationComplte and tooltipevents. 
onAnitmationComplete calls the method to show the tooltips like a hover event does. 
Normally you define the events in tooltipevents to display the tooltips but we need to remove them and pass an empty array.
Note:(http://www.chartjs.org/docs/#doughnut-pie-chart). 
Javascript:
var options = 
{
    tooltipTemplate: "<%= value %>",
    onAnimationComplete: function()
    {
        this.showTooltip(this.segments, true);
        //Show tooltips in bar chart (issue: multiple datasets doesnt work http://jsfiddle.net/5gyfykka/14/)
        //this.showTooltip(this.datasets[0].bars, true);
        //Show tooltips in line chart (issue: multiple datasets doesnt work http://jsfiddle.net/5gyfykka/14/)
        //this.showTooltip(this.datasets[0].points, true);  
    },
    tooltipEvents: [],
    showTooltips: true
}
var context = $('#chart').get(0).getContext('2d');
var chart = new Chart(context).Pie(data, options);  
HTML:
<div id="chartContainer">
    <canvas id="chart" width="200" height="200"></canvas>
</div>
Example Data: 
var data = [
    {
        value: 300,
        color:"#F7464A",
        highlight: "#FF5A5E"
    },
    {
        value: 50,
        color: "#46BFBD",
        highlight: "#5AD3D1"
    },
    {
        value: 100,
        color: "#FDB45C",
        highlight: "#FFC870"
    }
]
JSFiddle PIE:
http://jsfiddle.net/5gyfykka/
JSFiddle BAR/LINE:
http://jsfiddle.net/5gyfykka/14/