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By the early eighties, there were a variety of off-the-shelf sound chips suitable for use in home computers and arcade games.
What about 1977? That seems to have been just a little early; I'm not seeing any good off-the-shelf sound chips in that year. Are there any that I'm missing?
Sound generation might be easier using an IC, but unless you have a need for your product to be small, there's no reason you couldn't do it with a few discrete components and some general-purpose ICs. This article gives a few sample circuits that are useful for producing sounds, but note that for a computer there's another possibility that isn't considered here: you presumably already have a crystal oscillator to drive your clock signal, in the range of ~1-4MHz depending on the CPU you've chosen. Feeding that into a divider circuit (which is to say a counter and a digital comparator used to toggle a flip flop) and you can produce virtually any frequency output you like. Then to make sound, all you need to do is load the divider value into a latch that's connected to the processor bus, and use another bit to turn the sound on or off, and there you have frequency-controlled sound. It's not as good as the multi-channel sound chips you got later, but it's better than the Sinclair Spectrum had, and that managed OK even 5 years later...
I'm not sure about 1977. The first chips that come up to me are the TI TMS9919 aka SN76489 and General Instruments AY-3-8910. The AY-3-8910 was around for sure in 1978. Both were also used in a lot of arcade machines and consoles/home computers. And both have follow-up designs that are available even today.
The direct predecessor of the TMS9919 was the SN76477, called the Complex Sound Generator (the TMS9919 was called the Digital Complex Sound Generator). Each function could be controlled via direct inputs, so clearly a sound chip. But for use with digital systems, some glue logic (latches) would be needed. It got an article in Popular Electronics in 1978 but I don't know how long it was before it was available.
On the GI side, there were the AY-1-0212 and AY-3-214 before the AY-3-8910. But it's hard to qualify them already as sound chips, as they weren't really self-sufficient from today's view.
While the Signetics 2637 isn't 'just' a sound chip, it offered in 1977 a single sound chanel plus white noise and loudness controll. The 2637 could be best described as a single chip video console, as it includes a video circuitry with colour abilitiy and sprites, 13x16 text, character ROM plus definable characters plus ADC for up to 4 analoge paddles or two analogue joysticks - plus said sound generator.
Why specifically 1977?
A year later, but still in the seventies: General Instrument AY-3-8910, aka Yamaha YM2149F.
There was a game for the TRS-80 that used RF interference from the display as a sound source. You were instructed to place a radio next to the TV to hear sound.
Although it wasn't done often, it was possible in that era to build a rather powerful sound generator by combining a CPU, a ROM, a DAC, and maybe some RAM. The DAC need not be anything fancy--a bunch of resistors would suffice. I don't think Eugene Jarvis' 6800-based sound board goes back quite that far, but a 6502 running at 1.19Mhz with 128 bytes of RAM and two four-bit DACs (hardware found in an Atari 2600 from 1977) can produce four-voice music (61-note full chromatic scale) at a sample rate of 15.75KHz using 46 cycles out of every 76 for sound generation. A CDP1802 microprocessor might have been able to do likewise without needing any RAM if some creative addressing logic were wired in, but I don't know how the price of the 1802 would compare with that of a 6502 plus a RIOT (RAM+I/O+timer) chip.
"Sound chip" is an ambiguous term that has changed over time. There were audio DAC ICs available in the 1977 time frame. But the non-captive audio ICs did not include any DMA (there were no usable common bus standards at that time) or any significant DSP capabilities. But there were chips that produced a few "beeps" available near that time frame.
A capable "sound chip" at that time was more likely a large PCB for the S-100 bus or DEC minicomputer. Circa 1979 or '80, there were also some fairly full featured sound cards for the Apple II. But not chips.
