CHICAGO (CBS) — Only a month has passed since Illinois legalized civil unions, but more than 1,600 same-sex couples have already applied for licenses.

The gay rights advocacy group Equality Illinois says the large number of applications – 1,618, to be exact – shows how important the new law is.

The group found same-sex couples applied for license in 83 of the state’s 102 counties.

The legislation allowing for civil unions in Illinois was signed into law by Gov. Quinn on Jan. 31, after being approved by both houses of the state General Assembly in December.

The law went into effect June 1.

Civil unions give same-sex and opposite-sex couples the same rights as married couples when it comes to parenting, hospital rights, inheritances and more.

Both Gov. Quinn and Mayor Rahm Emanuel attended a gathering of 30 couples who exchanged vows in Millennium Park the day after civil unions officially became legal.

Since then, Mayor Emanuel has marched in the Gay Pride Parade – the first time a sitting mayor has appeared in the parade since retired Mayor Richard M. Daley participated in 1989.

In an interview with Wolf Blitzer of CNN late last month, Emanuel also expressed support for the same-sex marriage law that was recently approved in New York state, and said he hoped Illinois would also “move in that direction.”

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