Here is the sentence that includes the phrase.
なんと 忘れてしまった！ 格好だけに こうしちゃおれんな！
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こうしちゃおれん is a contraction of こうしてはいられない. It's used by an ojisan-type speaker. ては becomes ちゃ in colloquial speech. おれん is a colloquial negative form of おれる, which is a potential form of おる, which is a little dialectal variant of いる.
こうしてはいられない literally means "I/We cannot be doing this", but it's an idiom that means something along the lines of "It's of no use staying here", "We're wasting time now", "(I just noticed) I must handle this now".