Any dictionary should provide a perfectly reasonable definition for using chance as a verb. The OED provides several:
1. intr. To come about by chance; to happen, occur, fall out, come to pass.
a. with the event as subject, expressed either by a sb. preceding the verb, or by a clause following it, the verb being then preceded by it, as ‘It chanced that I saw’. arch.
† b. followed by an indirect obj. (dative); the event being expressed as in sense a, or by infinitive following it. Obs.
c. with the indirect object of sense b changed into grammatical subject; followed by inf. expressing the event. (e.g. ‘Him chanced to come’, ‘He chanced to come’: cf. happen.) Somewhat arch.
2. To happen to come, come by chance (on or upon; also formerly with other prepositions). Somewhat arch. (Cf. happen.)
† 3. To speed, have luck (of some kind). Obs.
4. a. trans. To risk, venture, take one’s chance of. colloq.
b. Slang phr. and chance the ducks: come what may; anyhow, anyway.
c. colloq. phr. to chance one’s arm: to perform an action in the face of probable failure; to take one’s chance of doing something successfully. Similarly to chance one’s mit.
¶ 5. how chance was formerly used in questions for ‘how chances it that’, ‘how is (was) it that’.
Here chance takes no inflexion, and almost assumes the character of an adverb. Cf. chance sb. C.
As sense 2 plainly explains, to chance that way means to happen to come that way, to come that way by chance.
The note “Somewhat archaic” tells you that the expression is today more apt to be encountered either in older works, or, if modern, in literary, oratorical, or poetic registers. Churchill is a modern writer albeit one well versed in English letters, and so to him it was not an inappropriate expression by any means. Indeed, he might well have used it not just in writing but in speech; after all, it is not all that archaic — merely “somewhat” so, a weak and tentative statement at most.