I'm not sure how canon this is, but apparently the Klingons got most of their current tech from aliens called the Hurq that invaded their world about 1000 years before TOS. That's how they got into space to begin with.
As far as I know, this is completely apocryphal and non-canon.
I remember hearing stories in fan circles about Klingon technology being stolen, as far back as the 1970's. At the moment, I can't find any reference to that notion in canon or in licensed TrekLit; it's not referenced in Memory Alpha or Memory Beta.
I wouldn't rule out fanzine published fan-fiction as the ultimate source of the notion of Klingon tech being stolen, but I'm not the expert on that and I don't really know.
The Hur'q are mentioned in only two episodes:
DS9: The Sword of Kahless
ENT: Affliction
I can't find any support in the episode transcripts for the notion.