Help with Windows 7 Drivers for HP Printers has several categories of assistance, with links.

One of the links is to Printers Supported in Windows 7. On this page, Deskjet and Inkjet printers that are supported are simply listed, but for LaserJet printers there is a link to a separate page:

Products Supported in Windows 7. Links at the top of this page are local links to locations on the same page, and include jumps to HP Laserjet printers, HP Color Laserjet printers, HP Laserjet Multifunction Printers. There is also a section on the kinds of drivers for the different ways the printers can be connected.

So far as I can find onthis last page, the HP 1320 printer is NOT SUPPORTED with a driver for Windows 7. IFF this printer can be used with Win7, you most likely will need to use one of the driver types briefly described near the bottom of thelast page above:

Descriptions of Windows 7 drivers

The following sections describe the drivers available for Windows 7.

Full solution CD (not likely)
This installation provides full product functionality and includes valuable software to help you get the most out of your product.

Full solution driver (not likely)
This driver provides full product functionality and does not require additional HP software.

Host Based driver (remotely possible?)
This driver uses your computer's resources to process print jobs, taking advantage of the computer's memory and processing power.

Host Based Plug and Play driver (maybe??)
This driver provides EZInstall to assist with installation for direct USB connections and provides basic printing functionality. It uses your computer's resources to process print jobs, taking advantage of the computer's memory and processing power.

In-OS driver (most likely if anything is going to work)
A full feature software and driver package for Windows 7 is not available for your product. However, the Windows 7 operating system installed on your computer contains a basic driver solution for your product. With the basic driver, some of the advanced product features are not available. You can print from a software program, and import and view images on a memory card, if your product has a memory card slot. With this basic driver, the buttons on the product do not function and some of the advanced product features are not available.

Universal Print Driver (possible, maybe, but intended for networked printers of mixed types and may require complex setup)
This driver works with a broad range of networked and direct-connected HP products, and is designed to simplify the task of managing multiple devices with the use of a single driver.

A separate look at the product specification for the HP LaserJet 1320 Printer series shows (Table on page 2 at "Interface and connectivity")

The "basic" HP 1320 with USB (serial port) and IEEE parallel port.

The HP 1320n/tn with USB or Ethernet (RJ-45) connection

The HP 1320nw with USB, RJ-45 Ethernet, and 802.11 b/g wireless connectivity

For full function, you would want to use the driver for the connection type you use, but since there isn't a full function Win7 driver for this printer it probably doesn't matter which might give you basic functionality.

This was an excellent home-office printer once upon a time. The "PostScript Emulation" is a little short of being full "PostScript Capable" but the difference probably wouldn't have mattered to anyone not working in commercial publishing. For its day, it was fast, but so far as Win7 is concerned you likely can just play taps and pull down the window shades so the neighbors won't see what you do (with it or otherwise) at night. Win7 does offer a "Run as WinXP" mode that might let you use a WinXP driver, but I haven't found that a convenient way of salvaging legacy stuff. YMMV.

John