Hi David, がis correct. With the word 上手 we use が。

As a note. 私は料理が上手です is NOT an omitted form of 私は料理を作るのが上手です。 私は料理が上手です is a complete sentene like : - 私は野球が好きです。 - 田中さんは、英語が上手だ - 佐藤さんは、裁縫が得意だ - あの人は泳ぎがすごい - 職人は手先が器用 - ゾウは鼻が長い - ニホンザルは芋洗いが上手 - 今度のデミオは走りがすごい

Hi! 私は料理が上手です is the correct expression. You're stating "I'm good at cooking" in a direct sense. Compare it to this sentence:　私は料理を作るのが上手です。Literally translated: "I'm good at making food". As you can see, we used を after 料理 because of the verb 作る. But since (料理) is something which is naturally "made or cooked", we don't have to mention the verb (作る). Therefore it's more preferable to use the sentence: 私は料理が上手です。

が is correct. good luck!