You can try a couple things. Fall back and take a dragon, OK it's expensive but nothing puts the fear into an enemy faster than that thing. You're now faster than anything he has (unless he takes a dragon) and the only thing really going to touch it are the Bolt Throwers. To counter the Bolt Throwers another way a Lord or Sorc Lord on a Disc is a very fast way of getting to the Reapers and taking them out, you cause fear meaning he may not even attack you back and all Chaos characters are good in combat. You can load him out with the armour of "I only ever take one wound from any source and am immune to killing blow" and/or the "3+ ward save vs shooting" to make those Bolt thrower shots next to useless as he cruises in to take them out.
There are a number of nasty units so you really want to try and force him to prioritise targets so that something is going to hit his lines. You can

Marauders and fitting in at least 2 units of Knights shouldn't be an issue, warhounds can also flank to go after those bolters. I know it sounds odd with Chaos but you almost want to try a target saturation approach, make him have a really hard time in deciding what to take out. You ideally want them to be reacting to what you are doing rather than dictating the flow of battle. Things like Giants and Shaggoths are also useful to soak up some firepower and pull it away from you units. OK, you might lose a 200pts model but it is normally going to take two turns to do it by which time you're combat troops should be hitting their lines. If they split between everything then you're going to bring a lot more power to bear when EVERYTHING hits their lines.