CPD did not provide any additional information about the person in custody Wednesday afternoon.
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Sierra Jamison's mother found her about 7:30 p.m. in a garage outside the home she had been renting in the 7800-block of South Indiana Avenue.
Her family said they believe they know who killed her and said they have shared that information with police.
"So I guess he couldn't take the rejection? I guess he took it out in a way he shouldn't as a man," Jamison's aunt Carmella Williams said.
The Cook County Medical Examiner's Office said Jamison's cause of death was strangulation.
Her mother said her daughter had just celebrated her 30th birthday and was working as a phlebotomist.
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She was ambitious, and about to start nursing school, her family said.
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"Sierra was a hard-working, independent young woman. She had goals and dreams," Williams said.
She said her niece also made family her top priority.
Jamison's mother said she was renting the home from a former co-worker and was looking to move. She leaves behind a 6-year-old son.
Jamison had also moved her mother and two younger sisters in to live with her and her son.
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"Her daily routine was coming home, getting off work, coming in to meet and greet everybody in the house, love on her son," Williams said.
Jamison's family was in the home Monday evening, but she never made it in the house.
The family is planning to hold a balloon release at 6:30 p.m. Wednesday in the 4500-block of West Jackson Boulevard.
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