A gentle, warmhearted immigrant comedy that’s rarely more than mildly amusing, “The Tiger Hunter” follows Sami (Danny Pudi), an aspiring engineer, from his rural Indian village to a job opportunity in Chicago.

The year is 1979, the fashions are horrendous and Sami has but two ambitions: To win the love of his childhood sweetheart and achieve the social status of his father, a celebrated tiger hunter who died when Sami was a child. Problems arise immediately when an expected engineering position disappears in a downsizing company, leaving Sami with a temporary job as a draftsman and a visa that’s set to expire in 30 days.

With a likable cast and a wholesome message about the true meaning of success, “The Tiger Hunter” might balk at the harsher details of immigrant life, but it has a generosity of spirit that lifts everyone up. Surrounding Sami with a strong support group of fellow South Asian professionals working menial jobs, the director, Lena Khan (who wrote the script with Sameer Gardezi, and whose own grandfather was a tiger hunter), knows exactly the story she wants to tell.

She is helped immensely by Mr. Pudi, whose quirky performance as a television-obsessed student on the NBC comedy “Community” was a consistent delight. It also gave him an ease with ensemble work that allows him to blend with other actors instead of sucking attention. The result is an endearingly old-fashioned comedy, not just in its style and the sweetness of its plot, but also in its bright-eyed optimism about immigrant opportunities. These days, it can be hard to remember that for those who dreamed large, America once seemed like a soft place to fall.