What's the meaning of this?
Is it something like don't fool me?
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This 吃 means to take.
Example 1: Chess game 西洋棋
If you take (attack) my knight, I will take (attack) your queen.
Example 2: Go game 圍棋
I dare you to take (capture) that stone, otherwise I will take (capture) your whole piece of stones.
Example 3: Business competition 商業競爭
You should not dare to take (occupy) my company, or I will sue you and make you bankrupt.
Example 4: underworld 黑道
double cross; stealing from thieves; dog eats dog
Therefore, we can treat 我 in 你不敢吃我 as a pronoun. It means my stuff, 我的某樣東西. The real object of this sentence is the stuff, 某樣東西.
Check your context, and you should be able to find the real object, which is not 我 (me).
You dare not take my stuff.
Another possibility is to bully, 欺壓 or 欺負.
I dare you to bully me.