Chickens were called chicken before chickens were called fowl. Fowl emerged in early modern English, had a period of popularity, and then faded by the 20th century.
Chicken goes back to Old English, where it referred to the young of gallus gallus domesticus - the chick (Oxford English Dictionary, "chicken, n."). By the late 14th century, chicken was used to refer to the adult chicken as well as the meat:
1381 Diuersa Servicia in C. B. Hieatt & S. Butler Curye on Inglysch (1985) 64 Nym kedys or chekenys & hew hem in morsellys.
c1405 (▸c1387–95) G. Chaucer Canterbury Tales Prol. (Hengwrt) (2003) l. 382 To boille the chiknes [c1415 Corpus Oxf. chikenes, c1430 Cambr. Gg.4.27 chekenys] with the Marybones.
This usage continued to the present day. Certainly there are quotes in the 18th and 19th century that show chicken didn't fade from fashion entirely at any point:
1760 T. Warton Idler 26 Jan. 25 The Company may..refresh themselves with cold Tongue, Chicken, and French Rolls.
1881 Judy 30 Mar. 155/1 Sloper had roast chicken for dinner.
Fowl is also from Old English, but it referred to birds more generically ("fowl, n."). Only in the late 16th century did it emerge as a more specific term for domesticated birds like hens:
a1586 Sir P. Sidney Arcadia (1590) iii. xxiii. sig. Xx3 As folkes keepe foule, when they are not fatte inough for their eating.
By the 17th century fowl could refer to meat as well:
1672 O. Walker Of Educ. i. xii. 160 A feast suggests..Fish, Foul, Flesh.
The OED notes that this usage isn't current except in set phrases like "fish, flesh, and fowl."
What happened to fowl?
So chicken stayed around after fowl dropped off in usage. When did that happen? Perhaps in the early 20th century. For example, here is an NGram showing that chicken appears more in its corpuses after 1900:
As a coincidence, the OED entry for "chicken, n." also includes this quote from around the same time, which may suggest some middle-class snootiness toward fowl:
1908 Westm. Gaz. 24 Jan. 3/1 It is a disastrous betrayal of middle-class origin to speak of a ‘chicken’ as a ‘fowl’. Whatever the age of the bird, the word must always be chicken.
One quote doesn't prove any causality, though. It is also possible that farmers and grocery stores themselves tended toward chicken to refer to the specific animal and its meat, whereas fowl persisted in a more generalized form to refer to wild fowl or water fowl.