Before I start I must warn you that colour is very
technical as it is an inherited genetic function!
Ok, as a quick biology lesson when the male sperm and female egg 'meet' they effectively (a lot more technical than this) form one completely new and unique cell whereby the genes from the male are mixed with the genes from the female. The foal's characteristics will then be determined from the dominance of the resultant genes. However, another problem that arises during the process of sex cell production (gametes - egg, sperm) is that the production of these cells involve a special type of division known as meiosis
. Basically, a sex cell contains 23 chromosomes rather than 46 which would be the number in a normal cell. In this process the genes are effectively split randomly between paternal and maternal genes of the mother/father genetic make-up - this produces "unique" sex cells which as a resultant will create a unique foal.
So what does this mean? Well... it basically means that foal colour is somewhat random in character although it is possible to give a probability of a foal having a certain colour - if both parents are chestnut chances are that the foal will be chestnut too. However, if the parent's parents were both bay then there is a probability that the foal could be palomino also.
Back to the biology! The specific 'coding' which determines various characteristics are referred to as alelles and for simplicity it is said that one allelle for a characteristic will come from father and the other will come from mother (hair colour is actually polygenuous but nvm) and from these hair colour is determined. Now as I mentioned earlier the actual allelles involved are 'random' but you can know which allelles are involved if you have taken a genetic profile or if you have a history of the colours in the breeding line.
Furthermore, allelles can also be dominant or recessive in character. If they are dominant then when the resultant allelles are 'heterogenuous' then it will be this characteristic which shows on the 'phenotype' - the one that gets displayed.
From this you can construct what is known as a 'punnett square' which gives both allelles of the parent's:
As you can see from the square above the dominant allelle is A and as a result all offspring will be red.
However, if both parent's are heterogenous red then there is a 1 in 4 possiblity that the offspring will be blue.
To go specifically to your case... it doesn't really matter that she is pure paint in colour terms as if they were varying colours then she will most probably have different possible colour combos in her genetic make-up. However, I believe (correct me if I'm wrong) that chestnut is a dominant allelle and so I would believe that it is probably more likely that the foal will be chestnut. Indeed, given that he has only thrown chestnut then it is likely that he is homogenous chestnut and then given that chestnut is dominant then this would make chestnut a practical certainty. HOWEVER, this still does depend on their bloodlines as while the statistics point towards homogenous it is still only an educated guess.