The Sky, at 605 W. 42nd St., will offer 235 below-market-rate apartments. View Full Caption Moinian Group

HELL'S KITCHEN —The lottery for affordable apartments in a new tower on the far West Side opened this week — with rents as low as $868 per month.

The Sky, at 605 W. 42nd St. near the West Side Highway, offers 235 below-market-rate apartments, including 70 studios for $868 per month, 120 one-bedrooms for $931 per month and 45 two-bedrooms for $1,124 per month, according to the Department of Housing Preservation and Development.

In order to be eligible to apply, households of four must make more than $39,978 and less than $51,780 for the two-bedroom units. Individuals must make at least $31,132 but no more than $36,300 for a studio, the agency said.

The 71-story building's amenities include a putting green, "water club" and fitness center, but the application shows that additional fees for those services might apply.

The apartments, which make up 20 percent of total units in the building, are part of a deal with the city that allows developer Moinian Group to build Manhattan’s largest residential building, Curbed reported.

The developerdeclined to comment.

Those interested can apply online or by mail.