> 本当は常連さんにだけのサービスなんだけど、お客様好みだからあたしおごっちゃう！

I know ちゃう comes from しまう  
ちゃう = when the verb ends with て = 食べて ＝たべちゃう じゃう = when the verb ends with で =
飲んで＝のんじゃう

て and で are already included and it is not necessary to put them

But I can't figure out which is the verb in おごっちゃう
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meaning
What is the meaning of おごっちゃう in this sentence
The verb that seems to be throwing you off is [奢る{おごる}(jisho.org's
definition)](https://jisho.org/word/%E5%A5%A2%E3%82%8B), a godan verb meaning
to pay for someone else's stuff, often a meal. Since it's a godan verb, the
te-form is おごって. From there you get おごっちゃう.

> あたしおごっちゃう  
>  It's my treat
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answer