Tums and similar antacids are almost entirely calcium carbonate. According to their website:

The active ingredient in TUMS is calcium carbonate from a mined calcium source. It may be an appropriate option for people who cannot consume calcium sourced from shellfish. Each tablet contains 1000 mg of calcium carbonate, 410 mg of elemental calcium, 5 mg of magnesium and 2 mg of sodium.

Mined and from shellfish sounds like chalk to me.

Sure enough, in their FAQ:

The calcium carbonate in TUMS antacid is processed from pure limestone, resulting in a high degree of purity.

Let's compare toothpaste, which one uses a small amount of twice a day and consumes (if old enough) almost nothing to an antacid made for occasional use but consumed in hundreds to thousands of milligrams at a time. Seems like there should be far more consumer concern about lead in antacids.

I found a paper about determining limits of lead detection in CaCO3, but they spiked lead into antacid tablets. There doesn't seem to be a whole lot of concern out there about all this lead in chalk.