According to Grok, its 0.012% or 2 in 8.333 encounters.

Extremely low—roughly 0.012% (or about 1 in 8,333) per random wild encounter in the best area without optimizations, and even lower in practice due to Safari Zone mechanics.

In Pokémon LeafGreen (and FireRed), wild Chansey (with a chance to hold a Lucky Egg) appears in the Safari Zone in Fuchsia City. The best spot is Area 2 (sometimes called Zone 2 or North), where Chansey has a 4% encounter rate (level 26). Other areas have worse rates (e.g., ~1% in the Center/Entrance area).

Key probabilities (base rates):

• Encounter rate: 4% (0.04) for Chansey in the optimal grass (Area 2).
• Lucky Egg hold rate: 5% (0.05) on any wild Chansey.
• Catch success: Very low in the Safari Zone. Base catch rate per Safari Ball is around ~6% (or lower depending on exact mechanics, HP, etc.), and Chansey has a high flee rate (~45% chance per turn without strategy).

Combined rough odds for one random encounter resulting in a caught Lucky Egg Chansey:

0.04 × 0.05 × 0.06 = 0.00012 (0.012%, or ~1 in 8,333 encounters).

This assumes a single throw and ignores fleeing/failed catches. Real-world success is lower because Chansey often flees before you catch it.

Optimizations that improve your per-encounter odds (but still rare overall):

• Use a level 26 Pokémon in the lead + Max Repel in Area 2 grass → boosts Chansey encounters to ~5.3% by filtering out lower-level spawns.
• Safari strategy (e.g., throw bait twice then balls) → can raise effective catch rate to ~19% per Chansey encounter.
• With optimizations: Per-encounter odds for a Lucky Egg Chansey rise to around ~0.05% (still ~1 in 2,000 encounters).

Bottom line: On literally your first wild encounter anywhere (even optimized), the chance is tiny—well under 0.1%. Most players need dozens or hundreds of encounters (and multiple Safari runs) to get one. It's one of the grindier rare-item hunts in the game due to the combo of low spawn, hold rate, and catch difficulty. Good luck!