Updated 09/08/11 – 12:42 p.m.

WHEATON, Ill. (CBS) — A convicted killer already serving a 60-year prison sentence for one murder has been sentenced to life in prison after admitting to the 1976 murder of nursing student Darlene Stack.

Michael Whitney, 58, entered his guilty plea Thursday morning, a month after DuPage County prosecutors charged him in Stack’s death. He was already in prison for the 1982 murder of Cecil Wallar and he was projected to be paroled in October 2012.

“Thirty Five years ago Darlene Stack’s life was viciously taken from her in her own home,” DuPage County State’s Attorney Robert Berlin said in a prepared statement. “It is my sincerest hope that while their pain may still linger, the family and friends of Darlene Stack may be able to finally close this horrible chapter of their lives.

Darlene Stack was raped and stabbed to death in a Wheaton boarding house in 1976.

As WBBM Newsradio’s Julie Mann reports, Stack, then 28, was sexually assaulted and stabbed 33 times in a Wheaton boarding house where she had been renting a room on Aug. 18, 1976.

LISTEN: WBBM Newsradio’s Julie Mann reports

The case remained open and unsolved until last month, when the DuPage County State’s Attorney’s office charged Whitney, who lived in the same boarding house.

Prosecutors said Whitney broke into Stack’s room on Aug. 18, 1976, after he had returned to the boarding house from a night of drinking. Once in Stack’s room, Whitney allegedly raped her and then stabbed her 33 times.

He allegedly left the house and tossed the murder weapon into the DuPage River that night. Stack was found naked in her bed that afternoon, bound and gagged with torn bed sheets.

Whitney had been the prime suspect from the beginning, but his girlfriend had provided an alibi in earlier years. The break came in 2005, when Wheaton police reopened the case and submitted semen-stained bed linens for DNA testing.

The girlfriend later admitted the alibi was a lie, and was granted immunity from prosecution.