Old English cealc "chalk, soft white limestone; lime, plaster; pebble," a West Germanic borrowing from Latin calx (2) "limestone, lime (crushed limestone), small stone," from Greek khalix "small pebble," which many trace to a PIE root for "split, break up."
Cognate words in most Germanic languages still have the "limestone" sense, but in English transferred chalk to the opaque, white, soft limestone found abundantly in the south of the island. The modern spelling is from early 14c. The Latin word for "chalk" was creta, which also is of unknown origin. With many figurative or extended senses due to the use of chalk marks to keep tracks of credit for drinks in taverns and taprooms, or to keep the score in games.
1570s, "to mix with chalk;" 1590s as "to mark with chalk," from chalk (n.). Related: Chalked; chalking. Old English had cealcian "to whiten." Certain chalk marks on shipped objects meant "admitted" or "shipped free," hence some figurative senses. Chalk boards also were commonly used in keeping credit, score, etc., hence figurative use of chalk it up (1903).