They have not. I can see this number cited on Chionis' Wikipedia page, but it is frankly mistifying for several reasons.

First, since the Ancient Greeks did not use the metric system, the precise measure of 7.05m must have been converted from ancient units of distance. Specifically, the Wikipedia page refers the reader to an online version of Eusebius' Chronicle (written in the 4th century AD), which appears to record under 664 BC that Chionis "could leap a distance of 22 feet." The problem is that the size of an ancient foot varied, from 29.5cm to as much as 32.4cm, and it is not clear which foot Eusebius was working with. Chionis' jump could have been anywhere between 6.51m to 7.13m depending on whether Eusebius was using Roman feet, the feet commonly used in Roman provinces, or some other measurement. Meanwhile, not a single known variation matches 705/22=32.04cm, so the cited jump length is wrong in all cases.

But it gets worse. I said above that Eusebius appears to record a 22ft jump because, to my knowledge, he actually doesn't. The evidence for Chionis and his Olympic achievements is gathered by Paul Christesen in 'Kings playing politics: the heroization of Chionis of Sparta' (Historia 59 (2010) 26-73) - including two passages that record the length of his jump. According to Christesen, Eusebius' Chronicle actually records a jump of 52ft (an incredible 15.34-16.85m). This number is corroborated by the other source, a fragment of Pseudo-Ioannis of Antioch, and seems to derive from a common source (the Olympic victor list of Sextus Julius Africanus, now lost). I do not know why the site linked above gives 22ft, but it seems likely that some editor or translator thought the actual number of 52ft was incredible and must be an error. The result is essentially a made-up number.

But that doesn't necessarily distinguish it from the number we do find in the sources. As Christesen points out, we should not take the ancient "records" of the first few centuries of the Olympic Games too seriously. In reality, the achievement of Chionis of Sparta was not recorded - anywhere, in any form - until the 470s BC, nearly two centuries after the event. Even when the Spartans did set up a monument to commemorate Chionis, they associated him primarily with the achievement of winning the stadion race and the diaulos race in several consecutive Olympic Games (Eusebius says 664, 660 and 656 BC, but Pausanias says he won 4 times starting in 668 BC). The victor list of Sextus Julius Africanus seems to be the earliest source that attaches Chionis to the long jump at all, let alone to a particular proficiency in it. In any case, since there were no records against which to corroborate them, none of these claims necessarily needed to be true as long as they were regarded as plausible.

None of this material is very good and to attach real numbers to Chionis' athletic achievements is ill-advised. As Christesen sums up (p. 67),

The most that can be said is that an individual named Chionis who came from Sparta probably won multiple Olympic victories at some point in the seventh century (...) Olympic victories, especially multiple victories by the same individual, were by their very nature memorable events, and there was an incentive for Chionis' family to keep alive the tradition about his feats of physical prowess. The recorded details of those feats, however, are very much open to question.