#Mathematica 62 64
Because this makes use of a native function, I appreciate all the more the beauty of shorter solutions from scratch. Output is 1002 chars long.
<< Combinatorica`
"79" <> DeBruijnSequence["0"~CharacterRange~"9", 3]
"799798787770760750740730720710980970960950940930920910108908708608508408308208889998988081009909008007006005004003002000190180170160150140130120119118117116115114113112912812712612512412312213913813713613513413313214914814714614514414314215915815715615515415315216916816716616516416316217917817717617517417317218918818718618518418318219919819719619519419319212111029028027026025024023022922822722622522422392382372362352342332492482472462452442432592582572562552542532692682672662652642632792782772762752742732892882872862852842832992982972962952942932322202103903803703603503403393383373363353349348347346345344359358357356355354369368367366365364379378377376375374389388387386385384399398397396395394343330320310490480470460450449448447446445945845745645546946846746646547947847747647548948848748648549949849749649545444043042041059058057056055955855755695685675665795785775765895885875865995985975965655505405305205106906806706696686679678677689688687699698697676660650640630620610790780779778978879"