A number of speculative birth times have been posted on the internet, but the one that seems most credible is 1:06 pm. This time was relayed by astrologer Frances McEvoy to astrology newsgroups, and supposedly originated from Obama's own memory when he was asked what time he was born during his New Hampshire visit. The indirect, unnamed sources mean that this data must be rated DD (for "dirty data") until confirmed by his birth certificate. However, the birth time sets the chart's angles, and from this, the astrologer can test it against the record. This process, known as rectification, relies on accurate angles, since major life events generally involve the Midheaven and Ascendant.
Obama's birth data (August 4, 1961; 1:06 pm; Honolulu, HI) places his Leo Sun near the Midheaven, and this position supports the "star quality" that so many observers report. His tenth house of career holds progressive Uranus and reform-minded Pluto, each of which describes a recognizable ideological facet of his professional persona. In addition, the tenth house Pluto opposes Chiron in the fourth house. This dynamic polarity involving the parental axis is about two degrees from exact, which by Solar Arc progression, coincides with the divorce of his parents when Obama was two (two degrees is two years).
So far, this 1:06 pm time feels right. Let's test it against some of Obama's personal history. On October 18, 1992, he married Michelle Robinson, who was working with a Chicago law firm. The main indicators for this kind of life change are evident: transiting Pluto was conjunct his Ascendant, and transiting Chiron was on his Midheaven. Transiting Vesta was precisely conjunct his Ascendant on the date he married, and this is significant because Vesta natally resides in the seventh house of partners. Most importantly, his progressed Midheaven was trine his seventh house Ceres, which is the strongest indicator yet that this data is correct. Ceres, now categorized as a dwarf planet, represents his partner as a caring person, financially secure (in Taurus), and the mother of his two children.