We present Atacama Large Millimeter Array (ALMA) 870-μm (345-GHz) observations of two submillimetre galaxies (SMGs) drawn from an ALMA study of the 126 submillimetre sources from the LABOCA Extended Chandra Deep Field-South Survey (LESS). The ALMA data identify the counterparts to these previously unidentified submillimetre sources and serendipitously detect bright emission lines in their spectra which we show are most likely to be [Cii] 157.74 μm emission yielding redshifts of z = 4.42 and 4.44. This blind detection rate within the 7.5-GHz bandpass of ALMA is consistent with the previously derived photometric redshift distribution of SMGs and suggests a modest, but not dominant (≲25 per cent), tail of 870-μm selected SMGs at z ≳ 4. We find that the ratio of L[C II]/LFIR in these SMGs is much higher than seen for similarly far-infrared-luminous galaxies at z ∼ 0, which is attributed to the more extended gas reservoirs in these high-redshift ultraluminous infrared galaxies (ULIRGs). Indeed, in one system we show that the [C ii] emission shows hints of extended emission on ≳ 3 kpc scales. Finally, we use the volume probed by our ALMA survey to show that the bright end of the [C ii] luminosity function evolves strongly between z = 0 and ∼4.4, reflecting the increased interstellar medium cooling in galaxies as a result of their higher star formation rates. These observations demonstrate that even with short integrations, ALMA is able to detect the dominant fine-structure cooling lines from high-redshift ULIRGs, measure their energetics and spatially resolved properties and trace their evolution with redshift.