This solution was provided by "Gina" Hoai-nam Hoang.  It's better than mine.

1	FILL 0
2	POKE 2
3	FILL 1
4	POKE 3
5	POKE 5 
6	POKE 6
7	FILL 23
8	POKE 8
9	PRINT "How many Fibonacci numbers do you want calculated? (1<=n<=23)"
10	GET
11	POKE 1
12	GTE 1 6
13	GOTO 17
14	PRINT "This number is less than 1."
15	FILL 1
16	GOTO 9
17	GTE 8 1 
18	GOTO 22
19	PRINT "This number is greater than 23."
20	FILL 1
21	GOTO 9
22	FILL 1
23	PUT
24	ADD 5 6
25	POKE 5
26	GTE 1 5
27	GOTO 29
28	QUIT
29	ADD 2 3
30	POKE 4
31	PEEK 3
32	POKE 2
33	PEEK 4
34	POKE 3
35	ADD 5 6
36	POKE 5
37	PEEK 4
38	PUT
39	GOTO 26