MapTool by RPTools is a Java-based tool that can do all of that, though it's a generic platform, so you'd have to build some of it yourself to get started. But it looks like someone has already created a Fate 3.0 generic framework that could give you a starting point.
MapTool has text chat built in, along with player-controlled tokens that have "Properties" defined by the GM (can keep track of player stats), has a die roller integrated into the chat window which includes Fudge dice rolling, and the map/token functionality can be used to create maps ahead of time with tiles/images, or draw freehand with paint tools to define areas. Additionally, MapTool tokens can have individual macros defined, so often-used rolls (skill checks) can be rolled easily with a button press.
I used OpenRPG prior to switching to MapTool, and MapTool is amazingly easy to set up (nothing to install; it's just a Java JAR) and use. Plus it has additional functionality like "status" indicators on tokens, life bars on tokens, vision/fog of war automation, spell templates, "hidden"/GM-only tokens (for hiding traps until they're visible), and more, if you want to use them.