The basilisk: one of the trickier creatures to balance. It's got six magical beast HD (above average as far as RHD go), but its ability scores are hilariously low, it is slow, its only natural weapon is a weak bite attack, and it's medium-sized. A 6th-level human fighter will be better at melee combat than a basilisk.
Of course, I didn't mention the eight-legged lizard's main appeal: its petrifying gaze. Anyone who looks at a basilisk has a chance of turning to stone. It doesn't even take an action, though you can spend one to repeat the attack, if desired.
On the one hand, being able to spam a save-or-kinda-die-but-not-quite that very few creatures (constructs, deathless, undead, and some celestials) are immune to every turn is cool, and the saving throw DC will be decent, despite a basilisk's lack of charisma. On the other hand, friendly fire is inevitable, and you don't want to accidentally petrify your entire party then die to a handful of grimlocks.
Finally, it is important to remember that while turning an enemy to stone is flashy, it's essentially no different from landing a boosted charge and OHKO'ing the foe. Both have their strengths and weaknesses, but in the end both remove foes from the battlefield. Petrification is strong, but so is a mid-level orc barbarian with the right feats.
With all this in mind, I consider the basilisk a creature that's barely too strong to lack a LA altogether, but is more-or-less appropriate with +1 LA. DM's are advised to exercise caution when allowing this race, though.
Basilisk, Abyssal Greater
As is so often the case with high-HD low-CR monsters, this one just fails to stack up to a PC of equal level. -0 LA: if you want to play this ask yourself if a normal basilisk won't do.