UPDATE chart.js 2.1 and above

var chart = new Chart(ctx, {
    ...
    options:{
        scales:{
            xAxes: [{
                display: false //this will remove all the x-axis grid lines
            }]
        }
    }
});


var chart = new Chart(ctx, {
    ...
    options: {
        scales: {
            xAxes: [{
                ticks: {
                    display: false //this will remove only the label
                }
            }]
        }
    }
});

Reference: chart.js documentation

Old answer (written when the current version was 1.0 beta) just for reference below:

To avoid displaying labels in chart.js you have to set scaleShowLabels : false and also avoid to pass the labels:

<script>
    var options = {
        ...
        scaleShowLabels : false
    };
    var lineChartData = {
        //COMMENT THIS LINE TO AVOID DISPLAYING THE LABELS
        //labels : ["1","2","3","4","5","6","7"],
        ... 
    }
    ...
</script>