We know that chloroform does not dissolve or mix with water. But why does chloroform, under some conditions, dissolve in a mixture of acidic acid and water?

Do you mean acetic acid?

whoops sorry, i think it is suppose to be acetic acid.

I would imagine that a small amount would dissolve due to the acetic acid (ethanoic acid) acting as a surface active agent. Chloroform is not totally insoluble in water anyway, solubility is about 0.8g/100g water.