As I thought, the DC conditions are totally wrong, it's only because you are feeding it a square wave that it looks to have low gain - it will actually be distorting and clipping on the HT rails (or at least on one of them).
To make it work properly you need to add a few extra parts.
1) Add a capacitor in series with R4, this will drop the DC gain to 1, and stop the feedback upsetting things.
2) Add two identical resistors on the input, one to +ve, and one to ground, this will bias the opamp midway between the supply rail and ground (effectively making a split supply). These set the input impedance of the stage, so you need to know how high it needs to be - I would suspect 100K each would probably be OK (giving a 50K input impedance).
3) Add a DC blocking capacitor in series with the input, this will stop the signal source affecting the DC conditions set by the two resistors.