diff --git a/Project.toml b/Project.toml
index 7a6df28b..fcd8841f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -39,9 +39,10 @@ julia = "1.10"
 Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 JET = "c3a54625-cd67-489e-a8e7-0a5a0ff4e31b"
+Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Dates", "DelimitedFiles", "JET", "OffsetArrays", "StableRNGs", "Test"]
+test = ["Dates", "DelimitedFiles", "JET", "Markdown", "OffsetArrays", "StableRNGs", "Test"]
diff --git a/src/statmodels.jl b/src/statmodels.jl
index b487a30e..28c2a477 100644
--- a/src/statmodels.jl
+++ b/src/statmodels.jl
@@ -147,8 +147,18 @@ function show(io::IO, ::MIME"text/plain", ct::CoefTable)
     nothing
 end
 
+# An unescaped `|` ends the cell it appears in, so a row containing one no longer
+# has the same number of cells as the alignment row and the table stops parsing as
+# a table at all. Callers hit this with the R-style `Pr(>|z|)` p-value header, and
+# with any string cell or row name that happens to contain a pipe. Same rule the
+# Markdown stdlib applies in `plain(::IO, ::Markdown.Table)`; applying it before
+# the column widths are measured keeps them consistent with what is printed.
+escape_markdown_pipes(s::AbstractString) = replace(s, '|' => "\\|")
+
 function show(io::IO, ::MIME"text/markdown", ct::CoefTable)
-    cols = ct.cols; rownms = ct.rownms; colnms = ct.colnms;
+    cols = ct.cols
+    rownms = escape_markdown_pipes.(ct.rownms)
+    colnms = escape_markdown_pipes.(ct.colnms)
     nc = length(cols)
     nr = length(cols[1])
     if length(rownms) == 0
@@ -157,7 +167,7 @@ function show(io::IO, ::MIME"text/markdown", ct::CoefTable)
     mat = [j == 1 ? NoQuote(rownms[i]) :
            j-1 == ct.pvalcol ? NoQuote(sprint(show, PValue(cols[j-1][i]))) :
            j-1 in ct.teststatcol ? TestStat(cols[j-1][i]) :
-           cols[j-1][i] isa AbstractString ? NoQuote(cols[j-1][i]) : cols[j-1][i]
+           cols[j-1][i] isa AbstractString ? NoQuote(escape_markdown_pipes(cols[j-1][i])) : cols[j-1][i]
            for i in 1:nr, j in 1:nc+1]
     # Code inspired by print_matrix in Base
     io = IOContext(io, :compact=>true, :limit=>false)
diff --git a/test/statmodels.jl b/test/statmodels.jl
index 70d864be..6f2da68c 100644
--- a/test/statmodels.jl
+++ b/test/statmodels.jl
@@ -1,6 +1,6 @@
 using StatsBase
 using StatsBase: PValue, TestStat
-using Test, Random, StatsAPI, LinearAlgebra
+using Test, Random, StatsAPI, LinearAlgebra, Markdown
 
 v1 = [1.45666, -23.14, 1.56734e-13]
 v2 = ["Good", "Great", "Bad"]
@@ -46,6 +46,24 @@ x3    1.56734e-13     Bad     2    0.00  <1e-15
 | [2] | -23.14        |    Great | 56 |   0.13 | 0.3467 |
 | [3] |   1.56734e-13 |    Bad   |  2 |   0.00 | <1e-15 |"""
 
+# Pipes in a header, a row name or a string cell must be escaped: an unescaped one
+# ends its cell, so the row presents more cells than the alignment row and the
+# whole thing stops parsing as a table. Downstream packages hit this with the
+# R-style `Pr(>|z|)` p-value header.
+ct_pipes = CoefTable(Any[v1, ["a|b", "Great", "Bad"], v3, v4, v5],
+                     ["Estimate", "Comments", "df", "t", "Pr(>|z|)"],
+                     ["x|1", "x2", "x3"], 5, 4)
+md_pipes = sprint(show, MIME"text/markdown"(), ct_pipes)
+@test occursin(raw"Pr(>\|z\|)", md_pipes)
+@test occursin(raw"x\|1", md_pipes)
+@test occursin(raw"a\|b", md_pipes)
+# Every row must present as many cells as the alignment row.
+let counts = [length(collect(eachmatch(r"(?<!\\)\|", row))) for row in split(md_pipes, '\n')]
+    @test all(==(first(counts)), counts)
+end
+# ... and the result must parse as a table rather than degrade to a paragraph.
+@test only(Markdown.parse(md_pipes).content) isa Markdown.Table
+
 @test length(ct) === 3
 @test eltype(ct) ==
     NamedTuple{(:Name, :Estimate, :Comments, :df, :t, :p),