A search for millimetric continuum emission from eight optically selected, radio-quiet quasars and a radio galaxy with 3.7 < z < 4.3 has been undertaken using a highly sensitive seven-channel bolometer on the IRAM 30-m Millimetre Radio Telescope. Detections of a potentially dust-rich quasar, and of 8C 1435 + 635, the most distant known radio galaxy, are reported. An extrapolation of the steepening centimetric radio spectrum of 8C 1435 + 635 accounts for less than 1 per cent of the observed 1.25-mm flux density, indicating that the emission is most likely from dust, although the present data cannot discriminate against synchrotron emission. If the emission is thermal, then the derived dust mass lies in the range 2 x 10(9) > M(d) > 8 x 10(7) M. for 20 < T-d < 100 K, or M(d) similar to 1.6 x 10(8) M. for T-d = 60 K, similar to that derived for 4C 41.17, suggesting a molecular gas mass of between 4 x 10(10) and 9 x 10(11) M.. The quasar, PC 2047 + 0123 at z = 3.80, has no detectable centimetric emission and the 1.25-mm continuum detected here probably also originates from 1.5 x 10(8) M. of dust (again for T-d = 60 K). Upper limits have been obtained for four quasars, corresponding to dust mass limits of about 3 sigma < 2 x 10(8) M.; less useful limits have been set for a further three quasars.