Present participle of chitchat; currently engaging in casual or trivial conversation.
From chitchat plus the present participle suffix -ing, forming the continuous aspect of the verb.
The double 't' in 'chitchatting' shows English's doubling rule in action—when a short verb has a short vowel, you double the final consonant before adding -ing, which makes the word sound even more like quick, repeated chatter!
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