Last night I was looking at NASA's equations for pressure and temperature of the atmosphere of Mars.
P (in kiloPascals) = $0.699 \exp^{-0.00009 h}$
The Valles Marineris is 11 kilometers deep at it's lowest point.
$P = 0.699 \exp^{(-0.00009) (-11000)} = $ 1.99 KPa = 0.28 psi
Correction: a commenter informed that Valles Marineries is 4.5 kilometers beneath "sea level" at it's lowest point. $P = 0.699 \exp^{(-0.00009) (-4500)} = $ 1.048 KPa = 0.15 psi
Then I looked up this chart of water boiling temperatures at low pressures, and saw that the boiling temperature of water in this pressure is a very reasonable, if slightly chilly $60^{o} F / 15^{o}C$
Correction: $45^{o} F / 7^{o}C$
I wonder if it's possible for surface water (rivers, lakes) on Mars at the bottom of the Valles Marineris?
Have we completely ruled it out with satellites surveying the region?
Would the relative dryness of the rest of the planet generally transport any water-bearing air in the region somewhere else (eventually drying the place out), or since it's at the bottom of a chasm, might the humidity remain?