How is "Free Grace Theology" linked with dispensationalism? I have a somewhat vague understanding of dispensationalism and Covenant theology, and have until now preferred the latter to the former because it seems simpler and hence more intuitive. I recently came across Free Grace Theology (FGT), which seems very appealing to me and, to my mind, focuses on the Gospel in a sharper way than either Reformed or Arminian theology. However, in watching talks by FGT people, I've noticed that they link FGT to dispensationalism in a very tight way, as if dispensationalism needs to be assumed in order to arrive at the Free Grace position. I would like to understand how and why this is the case, if it is true. Also, is FGT compatible with Covenant Theology?
The origin of today's "Free Grace Theology" movement is typically associated with Lewis Sperry Chafer, the famous dispensationalist, and one of its leading proponents has been Zane Hodges (of Dallas Theological Seminary, a major dispensationalist institution).  In Major Bible Themes, Chafer writes:


  The Scriptures are violated and the whole doctrine of grace confused when salvation is made to depend on anything other than believing. The divine message is not "believe and pray," "believe and confess sin," "believe and confess Christ," "believe and be baptized," "believe and repent," or "believe and make restitution." (Chapter 28)


This is a fundamental divergence from the historic Protestant doctrine of conversion, which sees both faith and repentance as necessary.  For more on the differences between these two approaches, see my answer to How does repentance fit into the doctrine of sola fide (“by faith alone”)?  

FGT flows naturally out of some varities of dispensationalism because of the clear dividing lines drawn between "law" and "grace," and "Old Covenant" and "New Covenant."  Covenant Theology sees them as more connected, arguing that both Old Testament and New Testament saints are saved the same way (the grace purchased by Jesus Christ on the cross) and that the law acts as a restraint, model, and guide for the church in all ages (both BC and AD).  This disagreement has led to debate over whether FGT is a form of the heresy antinomianism.

Incidentally, not all dispensationalists make such strong distinctions between law and grace, and thus not all are comfortable with FGT.  John MacArthur, a reformed baptist and dispensationalist, wrote the book The Gospel According to Jesus, in which he defends the traditional Protestant understanding.

As may now be clear, holding to both Covenant Theology and Free Grace Theology seems fraught with difficulty, though it wouldn't surprise me if some have tried.  Not only do the two views have different views of law and grace, but their doctrines of salvation diverge as well in areas like regeneration, conversion, and sanctification.  A Covenant Theologian would have to jettison quite a bit in order to accept FGT, at which point some would ask if the Covenant Theology label still has any meaning for that person.