Step 1: Collocation for the first blank. The standard phrase is \(\,\)\textit{head chef}\(\,\) (the senior cook in a kitchen), not “head chief.” Hence the first blank is chef.
Step 2: Spelling of the insect. The common noun is the closed compound housefly (like “butterfly”). Hyphenated “house-fly” or the open form “house fly” are variant/less preferred in general usage. As a simple object noun, housefly is appropriate.
Step 3: Combine. “The head chef was annoyed to see a housefly in the soup.”