Following the discovery by Djorgovski et al. (1985) of a companion to the high redshift quasar PKS 1614+051, we initiated a systematic search for such objects with the Danish 1.5 meter telescope at La Silla. The observing technique is CCD exposures in narrow filters (FWHM=100Å) centered on the redshifted Lyα. For an exposure time of 40 min. Our limiting magnitude is around 22.0 (where the r.m.s. error is approximately ±0.15), according to test runs with DAOPHOT. The aim of the search is to clarify the nature of such companions: are they “primordial” galaxies? Lyα clouds associated with the quasar? - and how frequent is such a phenomenon? Up to now we have covered 26 fields around quasars with redshift ≥3.0 (which is about 25% of all high redshift quasars in the Veron and Veron Catalogue). Furthermore 12 fields around z≈2.5 has also been observed (see Table 1). A quick visual inspection of all our frames has not revealed any companions except for the object found by Djorgovski et al. (which is easily picked up by our technique). However, a thorough photometric reduction (using DAOPHOT) might reveal fainter candidates. Taken together with the fields reported observed by Hu and Cowie (1987) and Djorgovski et al. (1987), a total of about 50 fields have so far been observed. The preliminary conclusion is therefore that such companions, whatever they might be, are very rare, and certainly much rarer than similar systems found around quasars of low redshift.