Chris Pine's in a court battle with his neighbor over the roots he's put down in L.A. -- roots that are allegedly infiltrating this woman's backyard ... and we mean that quite literally.

TMZ has obtained legal docs that show Chris ensnared in a showdown with someone named Helen Yu -- who lives next door to him in the Hollywood Hills ... and who's brought action against him for what she claims is destruction of her property due to his trees.

Long story short ... Yu alleges Chris has planted at least a dozen ficus trees at the border of his own home, but because these pesky plants have out-of-control roots ... she claims they've started to spread and encroach on her own parcel, and it's ruining her yard.

In the docs, she says she ended up suing Chris back in 2022 -- a lawsuit that flew under the radar -- but they quickly went into mediation, where they've been trying to work out a resolution to this behind closed doors.

Obviously, that isn't working out ... Helen says Chris seemed willing to settle this privately, until he ended up hurling another stone ... allegedly claiming Helen's fence was encroaching on his side of the property line.

They've been going back and forth ever since.

At this point, Helen says she's at her wit's end, with no resolution to the original problem -- namely, these freaking Ficus trees -- which she alleges have uprooted a lot of the concrete hardscape at her home, and infiltrated the actual foundation of her house.

In her docs, Helen says she was seeking around $267,000 to settle this with Chris -- while being open to giving him $75k for his own grievances, which her insurance company was going to handle -- but after Chris allegedly balked at that ... she's now asking for way more.

Helen says she now wants upwards of $346k -- covering the full cost to repair all the damages she claims she's endured -- and extra damages for infliction of emotional distress in the amount of an extra $225,000. So, in total, she wants around $571,000 from Chris.