Foal will be bay, black or chestnut, depending on several factors. Like Mehitabel says, mum can only pass on chestnut, so baby will have at least on chestnut gene. Mum might also have bay to pass on - the bay modifier is only visible on black based horses, so she could carry it without it being seen.
Dad has at least one bay gene, and at least one black - he could have two black or one black and one chestnut.
So - if dad passes on a black gene, foal will have a black base. If foal gets dad's bay gene as well, or one from mum we don't know about, it'll be bay, not black. If neither parent passes on bay though it would be black.
If dad has a chestnut gene to pass on, and baby gets that, it'll be chestnut, even if it gets bay as well.
It may or may not show sabino - sabino expresses best on chestnut coats, but can show up as a lip spot and socks, or roaning, or a wide blaze, or even big white splashes extending up the body, or any combination of those factors.
Every time I learn something new it pushes some old stuff out of my brain!