Beyond the giant planets there is a collection of bodies left over from the epoch of planet formation. The objects that are just beyond Neptune are more easily detected than those that journey hundreds of au away; all such highly eccentric objects have been observed inside 150 au. We are interested here in a population of Pluto to Mars-sized planets that were almost certainly present in the early Solar System, some of which may now be stranded in the distant Solar System. Using data from the Outer Solar System Origins Survey (OSSOS), which covers ~167 square degrees down to r ~25, we searched for objects beyond 300 au using a rarely used search technique. To find such objects we created catalogues of all the sources that were stationary (to the level of the astronomical seeing) in three images taken over 2 h. We then searched for which such 'stationary' objects were not present days/weeks/months before and after. Although other astronomical phenomena (e.g. supernovae) were discovered, no slow moving Solar System object was found. From the null detection and using a survey simulator, we obtain a model-dependent 95% upper limit of ~1000 on the number of 'planetary' objects (with absolute magnitudes, Hr, <2) in the distant Solar System. To our knowledge this is the first published limit for objects of this scale beyond 300 au. We show that if there are a small number of Mars-scale objects still in the distant Solar System, despite being brighter they may have escaped detection in other surveys due to their slow rates of motion.