The Church of Jesus Christ of Latter-day Saints (LDS) is using the Book of Mormon-proliferated belief that Mormons believe in a planet-based heaven as a teachable moment that doesn't totally dispel the rumor.
The popular Broadway show, currently in its third year, features a song performed by a Mormon missionary who includes the alleged afterlife planet in a number about his beliefs:
"I believe that God has a plan for all of us. I believe that plan involved me getting my own planet... I believe that God lives on a planet called Kolob."
The song "I Believe" also includes the line "I believe that in 1978 God changed his mind about black people," which is basically true, so we see why there might be some confusion about Kolob.
Kolob is mentioned in the Book of Abraham, a Mormon scripture that is part of the 'Pearl of Great Price,' which is canonized by the LDS. The Book of Abraham, penned by Church of Jesus Christ of Latter-day Saints founder Joseph Smith, purports to be the translation of ancient Egyptian texts describing the life of Abraham. Kolob is written about in Chapter 3:
And thus there shall be the reckoning of the time of one planet above another, until thou come nigh unto Kolob, which Kolob is after the reckoning of the Lord’s time; which Kolob is set nigh unto the throne of God, to govern all those planets which belong to the same border as that upon which thou standest. And it is given unto thee to know the set time of all the stars that are set to give light, until thou come near unto the throne of God.
Which essentially means that, if read literally, Kolob is a planet geographically close to God or where Mormons go in the afterlife. Because of this, Kolob has been repeatedly mentioned as one of the things Mormons believe -- something that Mormons, who are not concerned with the relatively obscure notion, don't appreciate. To combat the latest Book of Mormon-inspired batch of Kolob truthism, the church posted a 3,500-word essay rebutting the notion. In a post on the LDS Church's official website, "Becoming Like God," the author writes:
[Certain] limitations make it easy for images of salvation to become cartoonish when represented in popular culture. For example, scriptural expressions of the deep peace and overwhelming joy of salvation are often reproduced in the well-known image of humans sitting on their own clouds and playing harps after death. Latter-day Saints’ doctrine of exaltation is often similarly reduced in media to a cartoonish image of people receiving their own planets... while few Latter-day Saints would identify with caricatures of having their own planet, most would agree that the awe inspired by creation hints at our creative potential in the eternities.
So Mormons don't believe in heaven as planet per se, but they also don't not believe in it.
The Church of Jesus Christ of Latter-day Saints has been pretty savvy in its response to the play, which is not surprising. When the widely acclaimed satirical show came to Broadway in 2011, the Church issued a response that doubled as a plug for Mormonism, saying:
The production may attempt to entertain audiences for an evening, but the Book of Mormon as a volume of scripture will change people's lives forever by bringing them closer to Christ.
The Church has poured money into an advertising campaign in order to fix their "perception problem," pouring money into the "I'm a Mormon" campaign that features young, diverse Americans talk about their interests and ambitions before identifying as Mormon. And, of course, Mitt Romney's run for presidency did much to bring Mormonism into the mainstream.