JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://rawgit.com/nnnick/Chart.js/v1.0.2/Chart.min.js"></script>
<canvas id="myChart" width="400" height="200"></canvas>

JavaScript

var data = {
    labels: ["January", "February", "March", "April", "May", "June", "July"],
    datasets: [
        {
            label: "My First dataset",
            fillColor: "rgba(220,220,220,0.2)",
            strokeColor: "rgba(220,220,220,1)",
            pointColor: "rgba(220,220,220,1)",
            pointStrokeColor: "#fff",
            pointHighlightFill: "#fff",
            pointHighlightStroke: "rgba(220,220,220,1)",
            data: [65, 0, 80, 0, 56, 55, 40]
        },
        {
            label: "My Second dataset",
            fillColor: "rgba(151,187,205,0.2)",
            strokeColor: "rgba(151,187,205,1)",
            pointColor: "rgba(151,187,205,1)",
            pointStrokeColor: "#fff",
            pointHighlightFill: "#fff",
            pointHighlightStroke: "rgba(151,187,205,1)",
            data: [28, 48, 40, 0, 0, 0, 90]
        }
    ]
};

var ctx = document.getElementById("myChart").getContext("2d");
var myLineChart = new Chart(ctx).Line(data, {
    animation: false,
    onAnimationComplete: function () {
        // prevents the update from triggering an infinite loop
        if (!this.clearCycle) {
            this.clearCycle = true;
            
            this.datasets.forEach(function (dataset) {
                dataset.points.forEach(function (point) {
                    if (point.value === 0) {
                        point.display = false;
                        point.hasValue = function () {
                            return false;
                        }
                    }
                })
            })
            
            this.update();
        }
        else
            delete this.clearCycle;
    }
});