dhtmlxGantt

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DHTMLX Gantt is an open source JavaScript Gantt chart library that helps you illustrate and manage a project schedule in a nice-looking diagram.
It can show the dependencies between tasks as lines and allows you to set up different relationships between tasks (finish-to-start, start-to-start, finish-to-finish, start-to-finish). The Standard edition also inludes intuituve drag-n-drop interface and smart rendering which considerably boost performance while working with a large amount of tasks.
DHTMLX Gantt provides a flexible API and a large number of event handlers, which gives you the freedom to customize it for your needs. Moreover, the library comes with a comprehensive documentation and step-by-step video tutorials thus simplifying learning.
Getting started
Add files:
<script src="dhtmlxgantt.js" ></script>
<link rel="stylesheet" href="dhtmlxgantt.css" type="text/css">
Add markup: