Is it wise to use an Arduino to power a crystal oscillator?
Connect the clock input of the SN76489AN to OC4A or OC4B on the Arduino (pins 13 or 10). When the code on the Arduino starts up, configure the clock and pin to output a wave at the appropriate frequency.

PLLFRQ |= _BV(PLLTM1); // Enable PLL for high-speed timer 4
TCCR4A |= _BV(COM4A1) | _BV(PWM4A); // Configure OC4A for PWM operation
OCR4A = 8; // Set OC4A high for 9 cycles of a...
OCR4C = 17; // ... 18 cycle period
TCCR4B |= _BV(CS40); // Configure timer 4 for 64MHz


The code given will generate a 3.55556MHz square wave out of OC4A.