She is in critical condition at Jersey City Medical Center.
The chief says the other victims were being treated for lesser wounds. The attack occurred around 3 a.m. in the apartment of the second woman.
The man allegedly pulled out the machete after gaining entry to the apartment. Police say he attacked the second woman when she came out of a bedroom to see what was going on.
Union City is a densely populated community across the Hudson River from Manhattan.
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