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It happened at the Valley Terrace Apartments in the 2800 block of Chapel Hill Road shortly after 9 a.m.
Officials said the three victims included two men and one woman.
According to police, one man is in critical condition and the other two victims have non-life threatening injuries.
Police said the person of interest is an acquaintance of the victims and was a guest in the apartment. Officials said he fled the scene in a white vehicle.
The investigation is on-going.