The married couple - who have four-year-old daughter North and 22-month-old son Saint together - were allegedly targeted by an unnamed man on Friday (20.10.17) morning, when he broke into three cars at the bottom of the driveway at their gated Bel-Air property.
Sources tell TMZ.com the intruder was ''met with heavily armed Kardashian-West security'', which is believed to have become standard procedure since the 36-year-old reality star became the victim of an armed robbery whilst in Paris, France, last year.
TMZ also reports the intruder ''scampered away'' once he saw the armed guards, and police are now believed to be on the hunt for the alleged criminal.
According the publication, the only thing taken from the cars was an iPhone, which allegedly belongs to a member of the famous family's staff.
For 'Keeping Up with the Kardashians' star Kim, the alleged vandalism comes just one year after she was tied up in a bathtub in her hotel room in Paris and robbed of $10 million worth of jewellery.
And sources previously claimed the horrific ordeal has left her ''vulnerable''.
One source said: ''Kim has come a long way from the robbery but that said, it's a daily struggle to move past it and she probably never will be past it entirely.''
Whilst another added: ''Kim still speaks of the robbery as the most horrific experience she has ever had. [She] is still vulnerable and cries about the robbery.''
Kim previously revealed the ordeal left her fearing for her life, as she was terrified the robbers would shoot her if she attempted to escape during the attack.
She said: ''They ask for money. I said 'I don't have any money.'
''They dragged me out to the hallway, on top of the stairs. That's when I saw the gun like, clear as day. I was kind of looking at the gun, looking down back at the stairs...
''I had a split second in my mind to make this quick decision.
''Am I gonna run down the stairs... Either they're gonna shoot me in the back, or if I make it and they don't, if the elevator does not open in time, or the stairs are locked, then like, I'm f***ed. There's no way out.''
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