〜をおいて(他に)ない
no one / nothing but X
Noun + をおいて(他に)〜ない
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をおいて〜ない means "apart from X, there's nothing else", which strongly praises X as the only possible choice: この仕事を任せられるのは、彼をおいて他にいない, "there's no one but him I can trust with this job".
The noun is a person, a company or a time. The second half is 他にいない / 他にない / ない. With time words, it means "now or never": 今をおいてチャンスはない, "there'll never be a better chance than now".
It's formal and highly evaluative, common in recommendations and speeches. The verb 置く here means "to set aside", so it's literally "setting X aside, there's nothing".
Compare をもって (N1), "by means of", which looks similar but means something very different.
Examples
この仕事を任せられるのは、彼をおいて他にいない。
There's no one but him I can trust with this job.
日本でこの技術を持っているのは、この会社をおいてない。
No company in Japan but this one has this technology.
今をおいてチャンスはない。
It's now or never.
話し合うなら、今日をおいて他にない。
If we're going to talk, today is the only time.
リーダーにふさわしいのは、あなたをおいて他にいません。
There's no one more suited to be leader than you.