Context : Aims : Multiwavelength observations of the young massive cluster Westerlund 1 have revealed evidence for a large number of OB supergiant and Wolf-Rayet binaries . However , in most cases these findings are based on the detection of secondary binary characteristics , such as hard X-ray emission and/or non-thermal radio spectra and hence provide little information on binary properties such as mass ratio and orbital period . To overcome this shortcoming we have initiated a long temporal baseline , multi-epoch radial velocity survey that will provide the first direct constraints on these parameters . Methods : VLT/FLAMES+GIRAFFE observations of Wd1 were made on seven epochs from late-June to early-September 2008 , covering \sim 35 confirmed members of Wd1 and \sim 70 photometrically-selected candidate members . Each target was observed on a minimum of three epochs , with brighter cluster members observed on five ( or , in a few cases , seven ) occasions . Individual spectra cover the 8484-9001 Å range , and strong Paschen-series absorption lines are used to measure radial velocity changes in order to identify candidate binary systems for follow-up study . Results : This study presents first-epoch results from twenty of the most luminous supergiant stars in Wd1 . Four new OB supergiant members of Wd1 are identified , while statistically significant radial velocity changes are detected in \sim 60 % of the targets . W43a is identified as a short-period binary , while W234 and the newly-identified cluster member W3003 are probable binaries and W2a is a strong binary candidate . The cool hypergiants W243 and W265 display photospheric pulsations , while a number of early-mid B supergiants display significant radial velocity changes of \sim 15–25kms ^ { -1 } that we can not distinguish between orbital or photospheric motion in our initial short-baseline survey . When combined with existing observations , we find 30 % of our sample to be binary ( 6/20 ) while additional candidate binaries support a binary fraction amongst Wd1 supergiants in excess of \sim 40 % , a figure that is likely to increase as further data become available . Conclusions :