Applesoft BASIC, 21 bytes (tokenized)
0 PRINT 9 + 1: CALL 2066: END : OR <CTRL-F><CTRL-H>`
Replace <CTRL-F> and <CTRL-H> with their literal versions. Note that this only modifies the program in memory; re-loading it from the disk will reset the countdown.
Explanation
Sample run
]RUN
10
]RUN
9
]RUN
8
]RUN
7
]RUN
6
]RUN
5
]RUN
4
]RUN
3
]RUN
2
]RUN
1
]RUN
?SYNTAX ERROR IN 0
Explanation
PRINT 9 + 1 does what you'd expect. CALL 2066 calls the 6502 machine-language routine at memory location 2066, which is after END :. END halts the program so that the machine-language routine (which, to the Applesoft interpreter, is garbage) isn't executed.
The machine-language routine simply decrements the 9 in PRINT 9 + 1. Disassembly:
0812- CE 06 08 DEC $0806
0815- 60 RTS
After the counter reaches 0, it is "decremented" to /; attempting to run the program will then cause a syntax error.