I noticed recently that when the Doctor meets Missy and realizes she has two hearts, he says "You're a Time Lord." However, we know from "Listen" that "Time Lord" is a rank, not a species. So is the second heart unique to Time Lords? I can see why a second heart could be an advantage, especially to warriors.
What do you think of this theory? Is there any evidence against it? Is there evidence for it?
The second heart is common to all Gallifreyans. However, this does not invalidate the Doctor's statement, because he is meeting Missy off of Gallifrey, and among Gallifreyans only the Time Lords (and darned few of them) ever leave Gallifrey.
No, it's not unique.
HANDBOT: Statement rejected. Apalapucia is under planet-wide quarantine. This is a kindness facility for those infected with Chen Seven.
(The Doctor covers his mouth and nose with his coat lapel.)
DOCTOR: What?
RORY: Chen Seven, hmm?
DOCTOR: The one day plague.
RORY: What, you get it for a day?
DOCTOR: No, you get it, and you die in a day.
HANDBOT: There are forty thousand residents in the Twostreams Facility. Please remain in the sterile areas. Visiting hours are now.
(The Handbot beams itself away.)
DOCTOR: Sterile area. I'm safe.
AMY: What about me?
DOCTOR: Chen Seven only affects two-hearted races like Apalapucians.
So at least the Apalapucians have two hearts as well. And based on the same episode, they are humanoids too. So there has probably been other reasons how he recognised Missy as Time Lord. For example Time Lords telephatic ability to sense other Time Lords. (Seen at least in The End of Time parts 1 & 2 and in The Doctor's Wife)
It's possible, I don't think there is any evidence for or against it on the show, and other fiction like books and audios is apparently ambiguous on this point, see the binary vascular section of the Gallifreyan physiology article on the TARDIS wikia:
Gallifreyans naturally born before the time of Rassilon and Pythia had two hearts. (PROSE: Cat's Cradle: Time's Crucible, Lungbarrow)
Accounts differed as to the vascular systems of Gallifreyans in their first incarnation. Some accounts indicate that Gallifreyans normally had two hearts even in their first body. (AUDIO: Frostfire, TV: The Doctor's Daughter) Other accounts indicated that Gallifreyans Loomed after the Pythia's curse of sterility originally emerged with a single heart and gained their second only after their first regeneration, (PROSE: The Man in the Velvet Mask) while those of Newblood houses sprang from the Looms with two hearts from the outset. (PROSE: Christmas on a Rational Planet)
As an aside when Ian listens to the Doctor's chest in 'The Sensorites' he says that the heart beat (singular) sounds normal. John Peel (not the DJ, the author) suggests in his book 'The Gallifrey Chronicles' that this means that the second heart only appears after regeneration. Personally I feel it more likely that the first Doctor, who was aged and infirm at the time, may have lost use of his second heart. (In 'The Mind Of Evil' one of the Doctor's hearts stop after the attack by the Keller machine, and the Master has to restart it).
The Doctor's second incarnation (Patrick Troughton) had a medical check up in The Wheel in Space in 1968, there was no sign of a second heart then, either.
