If a program terminates and there is no one to see it, does it halt?
JavaScript, 39

(function f(x){for(;x!=++x;)f(x+1)})(0)


Explanation

Since JavaScript does not precisely represent large integers, the loop for(;x!=++x;) terminates once x hits 9007199254740992.

The body of the for loop will be executed Fib(9007199254740992) - 1 times, where Fib(n) is the nth fibonacci number.

From testing, I know my computer will do less than 150,000 iterations per second. In reality, it would run much slower because the stack would grow very large.

Thus, the program will take at least (Fib(9007199254740992) - 1) / 150000 seconds to run. I have not been able to calculate Fib(9007199254740992) because it is so large, but I know that it is much larger than 101000 * 150,000.

EDIT: As noted in the comments, Fib(9007199254740992) is approximately 4.4092*101882393317509686, which is indeed large enough.